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.
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:
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:
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) = -x^{ 2} + 1, find (f _{o} g)(x)
find (g∘f)(x) for x = 2 if f(x) = 2x +1 and g(x) = -x^{2}.
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.