Composition Of Functions Questions And Answers

Approved & Edited by ProProfs Editorial Team

The editorial team at ProProfs Quizzes consists of a select group of subject experts, trivia writers, and quiz masters who have authored over 10,000 quizzes taken by more than 100 million users. This team includes our in-house seasoned quiz moderators and subject matter experts. Our editorial experts, spread across the world, are rigorously trained using our comprehensive guidelines to ensure that you receive the highest quality quizzes.

Learn about Our Editorial Process

| By Themes

Themes

Community Contributor

Quizzes Created: 420 | Total Attempts: 905,690

Questions: 10 | Attempts: 620 | Updated: Jul 12, 2023

Questions

Settings

Feedback

During the Quiz End of Quiz

Difficulty

Sequential Easy First Hard First

Play as

Quiz Flashcard

Create your own Quiz

Share on Facebook Share on Twitter Share on Whatsapp Share on Pinterest Share on Email Copy to Clipboard Embed on your website

Do you know how to find the composition of functions? Can you solve these function composition questions and answers in this quiz? Go ahead then and check how good you are at solving mathematics problems. In mathematics, the composition of functions is an operation that is written inside another function. It takes two functions f and generates a new function; we can say h in such a way that h(x) = g(f(x)). Here, you have to solve function composition problems. Let's see if you can do that or not.

Questions and Answers

1.

Find the value of f(6) in f(x)=x²+3x-2

Explanation
To find the value of f(6), we substitute 6 into the function f(x)=x²+3x-2. Plugging in 6 for x, we get f(6)=6²+3(6)-2. Simplifying this expression, we have f(6)=36+18-2=52. Therefore, the value of f(6) is 52.

Rate this question:

1
4 0
2.

An electrician charges a base fee of $70 plus $50 for each hour of work. Write a function that shows the amount the electrician charges for every he works.

Explanation
The given function f(x)=70+50x represents the amount the electrician charges for every hour of work. The base fee of $70 is added to the product of $50 and the number of hours worked, x. This function calculates the total cost by multiplying the hourly rate by the number of hours worked and adding the base fee.

Rate this question:

1
4 0
3.

Given functions f(x) = 3x+½ and g(x)= 7+2x. Find f×g.
- A.
  
  F(x)=6x²+21x+2½
- B.
  
  F(x)=6x²+22x+3½
- C.
  
  F(x)=5x²+20x+2½
- D.
  
  None of these
Correct Answer
B. F(x)=6x²+22x+3½

Explanation
The given functions are f(x) = 3x+½ and g(x)= 7+2x. To find f×g, we need to substitute g(x) into f(x). Substituting g(x) into f(x), we get f×g = f(g(x)) = f(7+2x). Simplifying this expression, we get f×g = 3(7+2x)+½. Expanding and simplifying further, we get f×g = 21+6x+½. So, the correct answer is f(x)=6x²+22x+3½.

Rate this question:
4.

Given functions f(x) = 3x+½ and g(x)= 7+2x. Find f-g.
- A.
  
  F(x)=x-6½
- B.
  
  F(x)=x-5½
- C.
  
  F(x)=2x-6½
- D.
  
  F(x)=x+6½
Correct Answer
A. F(x)=x-6½

Explanation
The given functions are f(x) = 3x + 1/2 and g(x) = 7 + 2x. To find f-g, we subtract the two functions.

Subtracting g(x) from f(x), we get (3x + 1/2) - (7 + 2x).

Simplifying the expression, we combine like terms: 3x - 2x + 1/2 - 7.

This further simplifies to x - 6 1/2, which matches the answer choice f(x) = x - 6 1/2.

Rate this question:
5.

Given functions f(x) = 3x+½ and g(x)= 7+2x. Find f/g.
- A.
  
  F/g= (3x+1) /(7+2x)
- B.
  
  F/g= (3x+½) /(7+2x)
- C.
  
  F/g= (3x+½) /(6+2x)
- D.
  
  F/g= (3x-1) /(7+2x)
Correct Answer
B. F/g= (3x+½) /(7+2x)

Explanation
The given correct answer for f/g is (3x+1) /(7+2x). This is obtained by substituting the given functions f(x) = 3x+1/2 and g(x) = 7+2x into the expression f/g. By dividing the numerator (3x+1) by the denominator (7+2x), we get the desired result.

Rate this question:
6.

Given functions f(x) = 3x+½ and g(x)= 7+2x. Find f ∘ g.
- A.
  
  F ∘ g= 7x+21 ½
- B.
  
  F ∘ g= 6x+21
- C.
  
  F ∘ g= 6x+21 ½
- D.
  
  None of these
Correct Answer
C. F ∘ g= 6x+21 ½

Explanation
The composition of functions f ∘ g is found by substituting the expression for g(x) into f(x). In this case, g(x) = 7 + 2x. Substituting this into f(x) = 3x + 1/2 gives f ∘ g = 3(7 + 2x) + 1/2 = 21 + 6x + 1/2 = 6x + 21 1/2. Therefore, the correct answer is f ∘ g = 6x + 21 1/2.

Rate this question:
7.

Given functions f(x) = 3x+½ and g(x)= 7+2x. Find g ∘ f.
- A.
  
  G ∘ f=6x+8
- B.
  
  G ∘ f=6x+9
- C.
  
  G ∘ f=x+8
- D.
  
  G ∘ f=x-8
Correct Answer
A. G ∘ f=6x+8

Explanation
The composition of functions g ∘ f means that the output of function f is used as the input for function g. In this case, function f multiplies the input by 3 and adds 1/2, and function g multiplies the input by 2 and adds 7. Therefore, when we substitute f(x) into g(x), we get g ∘ f = 2(3x+1/2) + 7 = 6x + 1 + 7 = 6x + 8.

Rate this question:
8.

Given functions f(x) = 3x+½ and g(x)= 7+2x. Find f+g.
- A.
  
  F+g=5x+7 ½
- B.
  
  F+g=x+7 ½
- C.
  
  F+g=5x+7
- D.
  
  F+g=5x-7 ½
Correct Answer
A. F+g=5x+7 ½

Explanation
The given functions are f(x) = 3x+1/2 and g(x) = 7+2x. To find f+g, we need to add the two functions together. When we add the two functions, we add the coefficients of x and the constant terms separately. So, for the x term, we have 3x + 2x = 5x. For the constant terms, we have 1/2 + 7 = 7 1/2. Therefore, f+g = 5x + 7 1/2.

Rate this question:
9.

For f(x) = 2x + 3 and g(x) = -x² + 1, find (f _o g)(x)
- A.
 
 - 2x2+5
- B.
 
 2x2+5
- C.
 
 - 2x2+7
- D.
 
 - 2x2-5
Correct Answer
A. - 2x2+5

Explanation
The function (f o g)(x) represents the composition of functions f and g. To find (f o g)(x), we first substitute g(x) into f(x).

g(x) = -x^2 + 1

Substituting g(x) into f(x):

f(g(x)) = 2(-x^2 + 1) + 3
= -2x^2 + 2 + 3
= -2x^2 + 5

Therefore, the correct answer is -2x^2 + 5.

Rate this question:
10.

find (g∘f)(x) for x = 2 if f(x) = 2x +1 and g(x) = -x².
- A.
  
  20
- B.
  
  21
- C.
  
  25
- D.
  
  26
Correct Answer
C. 25

Explanation
To find (g∘f)(x), we need to substitute the value of x=2 into f(x) first. f(2) = 2(2) + 1 = 5. Then, we substitute this value into g(x). g(5) = -(5)^2 = -25. Therefore, (g∘f)(2) = -25.

Rate this question:

1
0

Quiz Review Timeline +

Our quizzes are rigorously reviewed, monitored and continuously updated by our expert board to maintain accuracy, relevance, and timeliness.

Current Version
Jul 12, 2023

Quiz Edited by
ProProfs Editorial Team
Jun 20, 2022

Quiz Created by
Themes

Composition Of Functions Questions And Answers

Find the value of f(6) in f(x)=x²+3x-2

An electrician charges a base fee of $70 plus $50 for each hour of work. Write a function that shows the amount the electrician charges for every he works.

Given functions f(x) = 3x+½ and g(x)= 7+2x. Find f×g.

Given functions f(x) = 3x+½ and g(x)= 7+2x. Find f-g.

Given functions f(x) = 3x+½ and g(x)= 7+2x. Find f/g.

Given functions f(x) = 3x+½ and g(x)= 7+2x. Find f ∘ g.

Given functions f(x) = 3x+½ and g(x)= 7+2x. Find g ∘ f.

Given functions f(x) = 3x+½ and g(x)= 7+2x. Find f+g.

For f(x) = 2x + 3 and g(x) = -x² + 1, find (f _o g)(x)

find (g∘f)(x) for x = 2 if f(x) = 2x +1 and g(x) = -x².

Composition Of Functions Questions And Answers

Find the value of f(6) in f(x)=x²+3x-2

An electrician charges a base fee of $70 plus $50 for each hour of work. Write a function that shows the amount the electrician charges for every he works.

Given functions f(x) = 3x+½ and g(x)= 7+2x. Find f×g.

Given functions f(x) = 3x+½ and g(x)= 7+2x. Find f-g.

Given functions f(x) = 3x+½ and g(x)= 7+2x. Find f/g.

Given functions f(x) = 3x+½ and g(x)= 7+2x. Find f ∘ g.

Given functions f(x) = 3x+½ and g(x)= 7+2x. Find g ∘ f.

Given functions f(x) = 3x+½ and g(x)= 7+2x. Find f+g.

For f(x) = 2x + 3 and g(x) = -x 2 + 1, find (f o g)(x)

find (g∘f)(x) for x = 2 if f(x) = 2x +1 and g(x) = -x2.

For f(x) = 2x + 3 and g(x) = -x² + 1, find (f _o g)(x)

find (g∘f)(x) for x = 2 if f(x) = 2x +1 and g(x) = -x².