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college algebra
College Algebra 11th Edition Michael Sullivan, Michael Sullivan III - Solutions
In Problems 37–56, write each expression as a sum and/or difference of logarithms. Express powers as factors. log x²³√x + 1] (x - 2)² x > 2
In Problems 51–58, use a calculator to evaluate each expression. Round your answer to three decimal places. In 3
In Problems 37–56, write each expression as a sum and/or difference of logarithms. Express powers as factors. x(x + 2) PL (x + 3)² log x > 0
In Problems 45–56, use transformations to graph each function. Determine the domain, range, horizontal asymptote, and y-intercept of each function.f(x) = 1- 2x+3
In Problems 37–56, write each expression as a sum and/or difference of logarithms. Express powers as factors. log5 √√√x² + 1 1 I-zx x > 1
The average annual cost of college at 4-year private colleges was $34,740 in the 2017–2018 academic year. This was a 3.6% increase from the previous year. (a) If the cost of college increases by 3.6% each year, what will be the average cost of college at a 4-year private college for the
In Problems 45–72, solve each exponential equation. Express irrational solutions in exact form.2x+1 = 51-2x
In Problems 39–50, find the domain of each function. f(x) Vln x
In Problems 45–56, use transformations to graph each function. Determine the domain, range, horizontal asymptote, and y-intercept of each function.f(x) = 2 + 4x-1
In Problems 39–50, find the domain of each function. g(x) 1 In x
In Problems 45–72, solve each exponential equation. Express irrational solutions in exact form.31-2x = 4x
In Problems 47–52, find functions f and g so that f ∘ g = H. E (₂x + 1) = (x)H
In Problems 45–56, use transformations to graph each function. Determine the domain, range, horizontal asymptote, and y-intercept of each function.f(x) = -3x + 1
In Problems 45–72, solve each exponential equation. Express irrational solutions in exact form.0.3 (40.2x) = 0.2
In Problems 45–56, use transformations to graph each function. Determine the domain, range, horizontal asymptote, and y-intercept of each function.f(x) = 3-x - 2
In Problems 45–72, solve each exponential equation. Express irrational solutions in exact form.5 (23x) = 8
In Problems 39–50, find the domain of each function. h(x) = log3 x-1)
In Problems 45–56, use transformations to graph each function. Determine the domain, range, horizontal asymptote, and y-intercept of each function. f(x) = 2x+2
In Problems 1–3, for each pair of functions f and g, find: f(x) = 3x - 5; g(x) = 1 - 2x2 (a) (fog)(2) (b) (gof) (-2) (c) (fof) (4) (d) (gog) (-1)
In Problems 32–35, for each function f:f(x) = 1 + 3-x (a) Find the domain of f. (d) Find f¹, the inverse function of f (b) Graph f (c) From the graph, determine the range and any asymptotes of f (e) Find the domain and the range of f¹. (f) Graph f-¹.
In Problems 32–35, for each function f:f(x) = 2x-3 (a) Find the domain of f (d) Find f¹, the inverse function of f (b) Graph f. (c) From the graph, determine the range and any asymptotes of f (e) Find the domain and the range of f-1. (f) Graph f-¹.
In Problems 32–35, for each function f: (a) Find the domain of f. (d) Find f¹, the inverse function of f (b) Graph f. (c) From the graph, determine the range and any asymptotes of f (e) Find the domain and the range of f-1. (f) Graph f-¹.
In Problems 32–35, for each function f:f(x) = 3ex-2 (a) Find the domain of f (d) Find f¹, the inverse function of f (b) Graph f. (c) From the graph, determine the range and any asymptotes of f (e) Find the domain and the range of f-1. (f) Graph f-¹.
In Problems 23–38, for the given functions f and g, find: State the domain of each composite function. (a) fog (b) gof (c) fof (d) gᵒg
In Problems 23–38, for the given functions f and g, find: State the domain of each composite function. (a) fog (b) gof (c) fof (d) gᵒg
In Problems 5–44, solve each logarithmic equation. Express irrational solutions in exact form. log₁/3 (x² + x) - log₁/3(x² − x) - x) = -1
In Problems 27–38, find the exact value of each logarithm without using a calculator. log V10
In Problems 29–36, determine whether the given function is linear, exponential, or neither. For those that are linear functions, find a linear function that models the data; for those that are exponential, find an exponential function that models the data. X -1 0 1 2 3 g(x) 6 1 0 3 10
In Problems 27–38, find the exact value of each logarithm without using a calculator. log V100
In Problems 5–44, solve each logarithmic equation. Express irrational solutions in exact form. loga (x - 1) loga (x + 6) = loga (x - 2) - loga (x + 3)
In Problems 27–38, find the exact value of each logarithm without using a calculator. log√₂4
In Problems 33–42, verify that the functions f and g are inverses of each other by showing that f(g(x)) = x and g(f(x) = x. Give any values of x that need to be excluded from the domain of f and the domain of g. f(x) = 32x; g(x) 2 (x-3)
In Problems 33–42, verify that the functions f and g are inverses of each other by showing that f(g(x)) = x and g(f(x) = x. Give any values of x that need to be excluded from the domain of f and the domain of g. f(x) = 4x8; g(x) 4 +2
In Problems 29–36, determine whether the given function is linear, exponential, or neither. For those that are linear functions, find a linear function that models the data; for those that are exponential, find an exponential function that models the data. X -1 0 1 2 3 F(x) -IN-1 -100 -- 16 32
In Problems 33–42, verify that the functions f and g are inverses of each other by showing that f(g(x)) = x and g(f(x) = x. Give any values of x that need to be excluded from the domain of f and the domain of g. f(x) = 2x + 6; g(x) = -x - 3 2
In Problems 27–38, find the exact value of each logarithm without using a calculator. log√39
In Problems 37–56, write each expression as a sum and/or difference of logarithms. Express powers as factors. log, 36x
In Problems 37–56, write each expression as a sum and/or difference of logarithms. Express powers as factors. X log3 9
In Problems 27–38, find the exact value of each logarithm without using a calculator. In Ve
In Problems 36–46, solve each equation. Express irrational solutions in exact form. 3x² + x = √3
In Problems 33–42, verify that the functions f and g are inverses of each other by showing that f(g(x)) = x and g(f(x) = x. Give any values of x that need to be excluded from the domain of f and the domain of g. f(x)= x³8; g(x) √x + 8
In Problems 37–56, write each expression as a sum and/or difference of logarithms. Express powers as factors. log, yo
In Problems 36–46, solve each equation. Express irrational solutions in exact form.86+3x = 4
In Problems 5–44, solve each logarithmic equation. Express irrational solutions in exact form.2 log5 (x - 3) log5 8 = log5 2
In Problems 39–50, find the domain of each function. f(x) = ln (x − 3)
In Problems 36–46, solve each equation. Express irrational solutions in exact form. 5x = 3x+2
In Problems 36–46, solve each equation. Express irrational solutions in exact form. 252 = 5-12
In Problems 37–56, write each expression as a sum and/or difference of logarithms. Express powers as factors. log7x³
In Problems 5–44, solve each logarithmic equation. Express irrational solutions in exact form.log3 x - 2 log3 5 = log3 (x + 1) - 2 log3 10
In Problems 39–50, find the domain of each function. F(x) = log₂ x²
In Problems 39–50, find the domain of each function. g(x) = ln (x - 1)
In Problems 36–46, solve each equation. Express irrational solutions in exact form. log3 Vx - 2 = 2
In Problems 27–38, find the exact value of each logarithm without using a calculator.ln e3
In Problems 5–44, solve each logarithmic equation. Express irrational solutions in exact form.2 log6(x + 2) = 3 log6 2 + log6 4
In Problems 5–44, solve each logarithmic equation. Express irrational solutions in exact form. 1) = log 2 1 3 log (x - 1)
If Tanisha has $100 to invest at 4% per annum compounded monthly, how long will it be before she has $150? If the compounding is continuous, how long will it be?
In Problems 39–46, show that (f ∘ g) (x) = (g ∘ f) (x) = x. f(x) = x³; g(x) = Vx
In Problems 5–44, solve each logarithmic equation. Express irrational solutions in exact form.3 (log7 x - log7 2) = 2 log7 4
In Problems 37–56, write each expression as a sum and/or difference of logarithms. Express powers as factors. In e X
In Problems 39–50, find the domain of each function. 084 (1-5) f(x) = 32 log4
If Angela has $100 to invest at 2.5% per annum compounded monthly, how long will it be before she has $175? If the compounding is continuous, how long will it be?
In Problems 39–50, find the domain of each function. H(x) = log5 x³
In Problems 39–46, show that (f ∘ g) (x) = (g ∘ f) (x) = x. f(x) = 9x - 6; g(x) =1/√(x + 6)
In Problems 36–46, solve each equation. Express irrational solutions in exact form. 8 = 4¹²¹.25x
In Problems 5–44, solve each logarithmic equation. Express irrational solutions in exact form.2 log13 (x + 2) = log13 (4x + 7)
In Problems 37–56, write each expression as a sum and/or difference of logarithms. Express powers as factors. In X et
In Problems 37–56, write each expression as a sum and/or difference of logarithms. Express powers as factors. In (xex)
In Problems 39–50, find the domain of each function. g(x) = 8 + 5 In (2x + 3)
In Problems 37–56, write each expression as a sum and/or difference of logarithms. Express powers as factors.ln(ex)
In Problems 36–46, solve each equation. Express irrational solutions in exact form. 2⁰.5 = 10⁰
In Problems 5–44, solve each logarithmic equation. Express irrational solutions in exact form. In x - 3V ln x + 2 = 0
In Problems 36–46, solve each equation. Express irrational solutions in exact form. log6 (x + 3) + log6 (x + 4) = 1
In Problems 37–56, write each expression as a sum and/or difference of logarithms. Express powers as factors. loga (u²v³) u>0, v> 0
In Problems 45–56, use transformations to graph each function. Determine the domain, range, horizontal asymptote, and y-intercept of each function. f(x) = 3 - 2
In Problems 5–44, solve each logarithmic equation. Express irrational solutions in exact form.(log3x)2 - 3log3 x = 10
In Problems 39–50, find the domain of each function. 1 (+) x + 1 f(x) = In
In Problems 39–50, find the domain of each function. In (15) g(x) = In
In Problems 37–56, write each expression as a sum and/or difference of logarithms. Express powers as factors. log₂ b² a> 0, b>0
In Problems 36–46, solve each equation. Express irrational solutions in exact form. el-x = 5
In Problems 37–56, write each expression as a sum and/or difference of logarithms. Express powers as factors. In(x² V1-x) 0
In Problems 39–46, show that (f ∘ g) (x) = (g ∘ f) (x) = x. x (x) 8 1 == 1 (x) f
In Problems 36–46, solve each equation. Express irrational solutions in exact form. 9 +4.33=0
In Problems 39–50, find the domain of each function. g(x) = logs x + 1 X
In Problems 45–56, use transformations to graph each function. Determine the domain, range, horizontal asymptote, and y-intercept of each function.f(x) = 2x + 1
In Problems 43–54, the function f is one-to-one. f(x) = x3 + 1(a) Find its inverse function f-1 and check your answer. (b) Find the domain and the range of f and f-1. (c) Graph f, f-1, and y = x on the same coordinate axes.
In Problems 37–56, write each expression as a sum and/or difference of logarithms. Express powers as factors. In (xV1 + x²) x > 0
In Problems 45–56, use transformations to graph each function. Determine the domain, range, horizontal asymptote, and y-intercept of each function.f(x) = 3x-1
A business purchased for $650,000 in 2010 is sold in 2013 for $850,000. What is the annual rate of return for this investment?
In Problems 23–38, for the given functions f and g, find: State the domain of each composite function. f(x) = 3x - 1; g(x) = x2 (a) fog (b) gof (c) fof (d) gᵒg
The logistic model Models the probability that, in a room of n people, no two people share the same birthday.(a) Use a graphing utility to graph P = P(n). (b) In a room of n = 15 people, what is the probability that no two share the same birthday? (c) How many people must be in a room before the
In Problems 23–38, for the given functions f and g, find: State the domain of each composite function. f(x) = x + 1; g(x) = x2 + 4 (a) fog (b) gof (c) fof (d) gᵒg
In Problems 14–19, solve each equation. Express irrational solutions in exact form. log₂ (x4) + log₂ (x + 4) = 3
In Problems 5–44, solve each logarithmic equation. Express irrational solutions in exact form. log x + log (x - 21) = 2
In Problems 5–44, solve each logarithmic equation. Express irrational solutions in exact form. 2 log3 (x + 4) - log39 = 2
In Problems 23–38, for the given functions f and g, find: State the domain of each composite function. f(x) = x2 + 1; g(x) = 2x2 + 3 (a) fog (b) gof (c) fof (d) gᵒg
In Problems 23–38, for the given functions f and g, find: State the domain of each composite function. f(x) = x2; g(x) = x2 + 4 (a) fog (b) gof (c) fof (d) gᵒg
In Problems 20–22, find the exact value of each expression. Do not use a calculator. log₂ 1 8
In Problems 14–19, solve each equation. Express irrational solutions in exact form. 4x³ Write log2 3x 18 logarithms. Express powers as factors. - - as the sum and/or difference of
In Problems 5–44, solve each logarithmic equation. Express irrational solutions in exact form. log2 (x + 7) + log2 (x + 8) = 1
In Problems 5–44, solve each logarithmic equation. Express irrational solutions in exact form. log (7x + 6) = 1 + log(x - 1)
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