The functions f and g are defined for x R by f: x x 1
Question:
The functions f and g are defined for x ∈ R by f: x ↦ x² −1 g: x ↦ 3x + 4
a) Find and simplify expressions for fg(x) and gf(x).
b) Hence find the values of a for which
fg(a) = 4a + gf(a).
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 55% (9 reviews)
ANSWER a To find fgx we need to substitute gx into fx so we get fgx f...View the full answer
Answered By
Churchil Mino
I have been a tutor for 2 years and have experience working with students of all ages and abilities. I am comfortable working with students one-on-one or in small groups, and am able to adapt my teaching style to meet the needs of each individual. I am patient and supportive, and my goal is to help my students succeed.
I have a strong background in math and science, and have tutored students in these subjects at all levels, from elementary school to college. I have also helped students prepare for standardized tests such as the SAT and ACT. In addition to academic tutoring, I have also worked as a swim coach and a camp counselor, and have experience working with children with special needs.
0.00
0 Reviews
10+ Question Solved
Related Book For
Complete Pure Mathematics 1 For Cambridge International AS & A Level
ISBN: 9780198427438
2nd Edition
Authors: Jean Linsky, Brian Western, James Nicholson
Question Posted:
Students also viewed these Mathematics questions
-
Functions f and g are defined on R by f (x) := x + 1 and g (x) := 2 if x 1 and g(1) := 0. lim g (f(x) g (lim f(x))
-
The functions f and g are defined for x R by f: x 3x + 2 g: x x + 1 a) Find the values of x for which fg(x) = gf(x). b) Find an expression for (fg) (x), stating its domain. c) Explain why (fg) ...
-
The functions f and g are defined for x R by f: x 4x 1 g: x 2x + k. Find the value of k for which fg = gf.
-
Use transaction analysis charts to analyze the following adjustments: a. Depreciation on equipment, $1,000. b. Rent expired, $600.
-
The following graph represents the results of a survey, conducted in May 2010, in which a random sample of adult Americans was asked, Please tell me whether you personally believe that in general...
-
Off the coast of Chile, a spotter plane sees a school of tuna swimming at a steady 5 km/h northwest (Figure). The pilot informs a fishing trawler located 100 km due south of the fish. The trawler...
-
What is the main difference in the nature of the frequency equations of a discrete system and a continuous system?
-
1. Develop a flight operations map that still serves each of the nine cities, but maximizes the companys profit per passenger. 2. Comment on how the 16 jets should be assigned. Northeastern Airlines...
-
A standard adult volleyball net has a height of 7 feet 4 1/8 inches which is shown as h in the sketch. The top of this net is supported by two ropes OA and OB with the dimensions shown. Find: Find...
-
Andy and Marcia Tufts, both age 35, are married with two children and file a joint return. Assume the children do not qualify for the child tax credit (Ch. 9), and the mortgage is not over $750,000....
-
a) If f (x) = 5, find the value of x. b) Show that ff (x) = x. f(x) = x/ x +3 , x R, x 3.
-
For each of the following functions state i) The greatest possible domain for which the function is defined ii) The corresponding range of the function iii) Whether the function is one-to-one or...
-
An order for an automobile can specify either an automatic or a standard transmission, either with or without air-conditioning, and any one of the four colors red, blue, black or white. Describe the...
-
Refer to the data set weather.csv. Can you conclude that the proportion of times the record maximum has occurred after 1945 is greater than the proportion of times the record minimum has occurred...
-
The queue is implemented as a class containing an array of items, a data member indicating the index of the last item put on the queue (rear), a data member indicating the index of the location...
-
Describe the accessing protocol of a queue at the abstract level.
-
The article "Weekly Personal Ozone Exposure and Respiratory Health in a Panel of Greek Schoolchildren" (A. Karakatsani, E. Samoli, et al., Environmental Health Perspectives, 2017, online) describes a...
-
A stack of integer elements is implemented as an array. The index of the top element is kept in position 0 in the array, and the stack elements are stored in stack[1].. stack[stack[0]}. 1. How does...
-
An aqueous solution is made from 0.798 g of potassium permanganate, KMnO4. If the volume of solution is 50.0 mL, what is the molarity of KMnO4 in the solution?
-
Find the equations of the ellipses satisfying the given conditions. The center of each is at the origin. Passes through (2, 2) and (1, 4)
-
Perform the test in Problem 10.21 and report a p-value (two-tailed). Interpret your results in words? Otolaryngology Many children have tympanostomy tubes surgically inserted in their ears to reduce...
-
Test whether the distribution of stage of disease is significantly different between Caucasian and African American women with breast cancer who are younger than 50 years of age. Please provide a...
-
Test whether the 5-year survival rate for breast cancer is significantly different between African American and Caucasian women who are younger than 50 years of age and have localized disease....
-
A company will be paying a dividend of $6.00 next period. if the cost of equity is 13%, what would be the approximate price of this stock today if the company is expected to grow at 4% for the...
-
21. Mr. Montzingo has the following auto insurance policy 50/100/25. Mrs. Yanzick and Mrs. Wooster are on their way to the dance club when Mr. Montzingo hits their car. It is Mrs. Wooster's car and...
-
The real risk free rate if interest is 4% (k*), Inflation Premium expected for the next 10 years is 3 % and the Maturity Risk Premium is equal to 0.1(t-1)% where "t" is equal to a security's maturity...
Study smarter with the SolutionInn App