Questions and Answers of Financial Accounting Information For Decisions

a. Sketch the graph of y |2x - 5|, showing the coordinates of the points where the graph meets the coordinate axes.b. Solve |2x - 5| = 3.
The function f is defined by The function g is defined by g(x) = 10/x - 1 for x > 0.Find gf(18). f(x) = 1+ Vx - 2 for x 2.
Solve each of the following pairs of simultaneous equationsa. y = x + 4y = |x2 - 16|b. y = xy = |3x - 2x2|c. y = 3xy = |2x2 - 5|
Find an expression for f-1(x). f(x) = 8 - Vx – 3 for x 3.
Given that each of these functions is defined for the domain - 3 ≤ x ≤ 4, find the range ofa. f: x → 5 - 2xb. g: x → |5 - 2x|c. h: x → 5 - |2x|
g(x) = x2 - 1 for x ≥ 0.Sketch, on a single diagram, the graphs of y = g(x) and y = g-1(x), showing the coordinates of any points where the curves meet the coordinate axes.
The function f and g are defined for real values of x bya. Find gf(37).b. Find an expression for f-1(x).c. Find an expression for g-1(x). f(x) = Vx – 1 -3 for x> 1, x - 2 g(x) = for x > 2. %3D 2х-
Determine whether each of these mappings is one-one, many-one or one-many.x → 1/x x ∈ R, x > 0
The function f is defined by f(x) - (x - 1)2 + 5 for x ≥ 1. Find the range of f.
The function f is defined by f(x) = (x - 1)2 + 3 for x > - 1.The function g is defined by g(x) = 2x + 4/x - 5 for x > 5.Find fg(7).
Find the range of each function.f: x → 3 - 2x for - 1 ≤ x ≤ 4g: x → |3 - 2x| for - 1 ≤ x ≤ 4h: x → 3 - |2x|
f: x → 5x - 3 for x > 0 g: x → 7/2- x for x ≠ 2Express f-1(x) and g-1(x) in terms of x.
f(x) = 4x - 2 for - 1 ≤ x ≤ 3.Sketch, on a single diagram, the graphs of y = f(x) and y = f-1(x), showing the coordinates of any points where the curves meet the coordinate axes.
A function g is such thata. Find the range of g.b. Find g-1(x).b. Find g-1(x).c. Write down the domain of g-1(x).d. Solve g2(x) = 3. g(x): 1 for 1 < x < 3. 2x-1
Determine whether each of these mappings is one-one, many-one or one-many.x → x2 + 1 x ∈ R, x ≥ 0
The function f is defined by f(x) = (2x + 1)2 - 5 for x ≥ - 1/2. Find the range of f.
h: x → x + 2 for x > 0.k: x → √x + 2 for x > 0.Express each of the following in terms of h and k.a. x → √x + 2b. x- Vx +2
a. Sketch the graph of y = |2x + 4| for - 6 < x < 2, showing the coordinates of the points where the graph meets the axes.b. On the same diagram, sketch the graph of y = x + 5.c. Solve the
f: x → (x + 2)2 - 5 for x > - 2a. Find and expression for f-1(x). b. Solve the equation f-1(x) = 3.
The function f is defined by f: x → 3 - (x + 1)2 for x ≥ - 1.a. Explain why f has an inverse.b. Find an expression for f-1 in terms of x.c. On the same axes, sketch the graphs of y = f(x) and y =
a. The functions f and g are defined, for x ∈ R, byFind fg(4).b. The functions h and k are defined, for x > 0, byExpress each of the following in terms of h and k.i.ii. x → x + 8iii. x → x2
Determine whether each of these mappings is one-one, many-one or one-many.x → 12/x x ∈ R, x > 0
The function f is defined by f: x → 10 - (x - 3)2 for 2 ≤ x ≤ 7. Find the range of f.
The function f is defined by f: x → 2x + 1 for x ∈ R.The function g is defined by g: x → 10/2-x for x ≠ 2.Solve the equation gf(x) = 5.
A function f is defined by f(x) = |2x - 6| - 3, for - 1 ≤ x ≤ 8.a. Sketch the graph of y = f(x).b. State the range of f.c. Solve the equation f(x) = 2.
f(x) = (x - 4)2 + 5 for x > 4a. Find an expression for f-1(x).b. Solve the equation f-1(x) = f(0).
f: x → 2x + 7/x - 2 for x ≠ 2a. Find f-1 in terms of x.b. Explain what this implies about the symmetry of the graph of y = f(x).
The function f is defined by i. Write down the range of f.ii. Find f-1(x) and state its domain and range.The function g is defined by g(x) = 4/x for - 5 ≤ x < - 1.iii. Solve fg(x) = 0. f(x)
Determine whether each of these mappings is one-one, many-one or one-many.x → ± x x ∈ R, x ≥ 0
The function f is defined by Find the range of f. f(x) = 3 + Vx – 2 for x 2.
g(x) = x2 + 2 for x ∈ R.h(x) = 3x - 5 for x ∈ R.Solve the equation gh (x) = 51.
a. Sketch the graph of y = |3x - 4| for -2 < x < 5, showing the coordinates of the points where the graph meets the axes.b. On the same diagram, sketch the graph of y = 2x.c. Solve the equation
a. The function f is such that f(x) = 2x2 - 8x + 5.i. Show that f(x) = 2(x + 1)2 + b, where a and b are to be found.iii. Hence, or otherwise write down a suitable domain for f so that f-1 exists.b.
f(x) = x2 - 3 for x > 0g(x) = 3/x for x > 0Solve the equation fg(x) = 13.
a. Sketch the graph of f(x) = |x + 2| + |x - 2|.b. Use your graph to solve the equation |x + 2| + |x - 2| = 6.
f(x) = x/2 + 2 for x ∈ R g(x) = x2 - 2x for x ∈ Ra. Find f-1(x)b. Solve fg(x) = f-1(x).
i. On the axes below, sketch the graph of y = 2 - x and y = |3 + 2x|.ii. Solve |3x + 2x| = 2 - x. 9- -6 6 x -9J
The function f is defined, for x ∈ R, by f: x → 3x + 5/x-2, x ≠ 2.The function g is defined, for x ∈ R, g: x → x -1/2.Solve the equation gf(x) = 12.
Solve the equation gf(x) = g-1(17).f(x) = x2 + 2 for x ∈ R g(x) = 2x + 3 for x ∈ R
f(x) = (x + 4)2 + 3 for x > 0g(x) = 10/x for x >0Solve the equation fg(x) = 39.
Solve the equation f(x) = g-1(x). 2x + 8 x - 3 f: xH for x + 2 Hx: 8 2 for x > -5 x - 2
The function g is defined by g(x) = x2 - 1 for x ≥ 0.The function h is defined by h(x) = 2x - 7 for x ≥ 0. Solve the equation gh(x) = 0.
f(x) = 3x - 24 for x ≥ 0. Write down the range of f-1.
The function f is defined by f: x → x3 for x ∈ R.The function g is defined by g: x → x - 1 for x ∈ R. Express each of the following as a composite function, using only f and/or g:a. x
f: x → x + 6 for x > 0 g: x → √x for x >0Express x → x2 - 6 in terms of f and g.
State which of the function f, g and h has an inverse.f: x → 3 - 2x for ≤ x ≤ 5g: x → |3 - 2x| for ≤ x ≤ 5h: x → 3 - |2x| for ≤ x ≤ 5
f(x) = x2 + 2 for x ≥ 0 g(x) = 5x - 4 for x ≥ 0a. Write down the domain of f-1.b. Write down the range of g-1.
The functions f and g are defined, for x ∈ R, by f: x → 3x - k, where k is a positive constant g: x → 5x - 14/x+1, where x ≠ -1.a. Find expressions for f-1 and g-1.b. Find the value of k for
Express each of the following as a composite function, using only f, g, f-1 and/or g-1:f: x → x3 for x ∈ R g:
Use the symmetry of each quadratic function to find the maximum or minimum points.Sketch each graph, showing all axis crossing points.a. y = x2 - 5x - 6b. y = x2 - x - 20c. y = x2 + 4x - 21d. y = x2
Solve the following simultaneous equations.y = x2y = x + 6
Sketch the graphs of each of the following functions.a. y = |x2 - 4x + 3|b. y = |x2 - 2x - 3|c. y = |x2 - 5x = 4|d. y = |x2 - 2x - 8|e. y = |2x2 - 11x - 6|f. y = |3x2 + 5x - 2|
Solve.a. (x + 3) (x - 4) > 0b. (x - 5) (x - 1) ≤ 0c. (x - 3) (x + 7) ≥ 0d. x(x - 5) < 0e. (2x + 1) (x - 4) < 0f. (3 - x) (x + 1) ≥ 0g. (2x + 3) (x - 5) < 0h. (x - 5)2 ≥ 0i. (x -
State whether these equations have two distinct roots, two equal roots or no roots.a. x2 + 4x + 4b. x2 + 4x - 21c. x2 + 9x = 1d. x2 - 3x + 15e. x2 - 6x + 2f. 4x2 + 20x = 25g. 3x2 + 2x + 7h. 5x2 - 2x
Find the values of k for which y = kx + 1 is a tangent to the curve y = 2x2 + x + 3.
Find the set of values of k for which the line y = k(4x - 3) does not intersect the curve y = 4x2 + 8x - 8.
Express each of the following in the form (x - m)2 + n.a. x2 - 8xb. x2 - 10xc. x2 - 5xd. x2 - 3xe. x2 + 4xf. x2 + 7xg. x2 + 9xh. x2 + 3x
f(x) = 1 - 4x - x2a. Write f(x) in the form a - (x + b)2, where a and b are constants.b. Sketch the graph of y = f(x).c. Sketch the graph of y = |f(x)|.
Solve.a. x2 + 5x - 14 < 0b. x2 + x - 6 ≥ 0c. x2 - 9x + 20 ≤ 0d. x2 + 2x - 48 > 0e. 2x2 - x - 15 ≤ 0f. 5x2 + 9x + 4 > 0
Solve the following simultaneous equations.y = x – 6x2 + xy = 8
Find the values of k for which x2 + kx + 9 = 0 has two equal roots.
Find the value of k for which the x-axis is a tangent to the curve y = x2 + (3 - k)x - (4k + 3).
Find the set of values of x for which x(x + 2) < x.
a. Express 2x2 - x + 6 in the form p(x - q)2 + r, where p, q and r are constants to be found.b. Hence state the least value of 2x2 - x + 6 and the value of x at which this occurs.
Express each of the following in the form (x - m)2 + n.a. x2 - 8x + 15b. x2 - 10x - 5c. x2 - 6x + 2d. x2 - 3x + 4e. x2 + 6x + 5f. x2 + 6x + 9g. x2 + 4x - 17h. x2 + 5x + 6
f(x) = 2x2 + x - 3a. Write f(x) in the form a(x + b)2 + c, where a, b and c are constants.b. Sketch the graph of y = |f(x)|.
Solve.a. x2 < 18 - 3xb. 12x < x2 = 35c. x(3 - 2x) ≤ 1d. x2 + 4x < 3(x + 2)e. (x + 3) (1 - x) < x - 1f. (4x + 3) (3x - 1) < 2x(x + 3)
Solve the following simultaneous equations.y = x – 1x2 + y2 = 25
Find the values of k for which kx2 - 4x + 8 = 0 has two distinct roots.
Find the values of the constant c for which the line y = x + c is a tangent to the curve y = 3x + 2/x.
Find the set of values of k for which the curve y - (k + 1)x2 - 3x + (k + 1) lies below the x-axis.
Express each of the following in the form a(x - p)2 + q.a. 2x2 - 8x + 3b. 2x2 - 12x + 1c. 3x2 - 12x + 5d. 2x2 - 3x + 2e. 2x2 + 4x + 1f. 2x2 + 7x - 3g. 2x2- 3x + 5h. 3x2 - x + 6
a. Find the coordinates of the stationary point on the curve y = |(x - 7)(x + 1).b. Sketch the graph of y =|(x - 7) (x + 1)|.c. Find the set of values of k for which |(x - 7) (x + 1)| = k has four
Find the set of values of x for whicha. x2 - 11x + 24 < 0 and 2x + 3 < 13b. x2 - 4x ≤ 12
Solve the following simultaneous equations.xy = 4y = 2x + 2
Find the values of k for which 3x2 + 2x + k = 0 has no real roots.
Find the set of values of k for which the line y = 3x + 1 cuts the curve y = x2 + kx + 2 in two distinct points.
Find the set of values of x for which x2 < 6 - 5x.
Express each of the following in the form m - (x - n)2.a. 6x - x2b. 10x - x2c. 3x - x2d. 8x - x2
a. Find the coordinates of the stationary point on the curve y = |(x + 5) (x + 1)|.b. Find the set of values of k for which |(x + 5) (x + 1)| = k has two solutions.
Solve.a. |x2 + 2x - 2| < 13b. |x2 - 8x + 6| < 6c. |x2 - 6x + 4| < 4
Solve the following simultaneous equations.x2 – xy = 0x + y = 1
Find the values of k for which (k + 1)x2 + kx - 2k = 0 has two equal roots.
The line y = 2x + k is a tangent to the curve x2 + 2xy + 20 = 0.a. Find the possible values of k.b. For each of these values of k, find the coordinates of the point of contact of the tangent with the
Find the values of k for which the line y = k - 6x is a tangent to the curve y = x(2x + k).
Express each of the following in the form a - (x + b)2.a. 5 - 2x - x2b. 8 - 4x - x2c. 10 - 5x - x2d. 7 + 3x - x2
a. Find the coordinates of the stationary point on the curve y = |(x - 8) (x - 3)|.b. Find the value of k for which |x - 8) (x - 3) = k has three solutions.
Find the range of values of x for which 4 3x2 < 0. 2х - 8
Solve the following simultaneous equations.3y = 4y – 5x2 + 3xy = 10
Find the values of k for which kx2 + 2(k + 3) x + k = 0 has two distinct roots.
Find the set of values of k for which the line y = k - x cuts the curve y = x2 - 7x + 4 in two distinct points.
It is given that f(x) = 4 + 8x - x2.a. Find the value of a and of b for which f(x) = a - (x + b)2 and hence write down the coordinates of the stationary point of the curve y = f(x).b. On the axes
Express each of the following in the form a - p(x + q)2.a. 9 - 6x - 2x2b. 1 - 4x - 2x2c. 7 + 8x - 2x2d. 2 + 5x - 3x2
Solve these equations.a. |x2 - 6| = 10b. |x2 - 2| = 2c. |x2 - 5x| = 6d. |x2 + 2x| = 24e. |x2 - 5x + 1| = 3f. |x2 + 3x - 1| = 3g. |x2 + 2x - 4| = 5h. |2x2 - 3| = 2xi. |x2 - 4x + 7| = 4
Solve the following simultaneous equations.2x + y = 7xy = 6
Find the values of k for which 3x2 - 4x + 5 - k = 0 has two distinct roots.
Find the values of k for which the line y = kx - 10 meets the curve x2 + y2 = 10x.
Given that the straight line y = 3x + c is a tangent to the curve y = x2 + 9x + k, express k in terms of c.
a. Express 4x2 + 2x + 5 in the form a(x + b)2 + c, where a, b and c are constants.b. Does the function y = 4x2 + 2x + 5 meet the x- axis? Explain your answer.
Solve these simultaneous equations.a. y = x + 1y = |x2 - 2x - 3|b. 2y = x + 4c. y = 2xy = |2x2 - 4| ア= 2 %3D X - 3

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