Question

Given the functions below, find f(g(x))

F(x)=x^2-x
G (x)=9-2x
(It’s on the picture) please need help asap!!!

Answer 1

option C:

4x² - 34x + 72

Explanation:

f(x) = x² - x

g(x) = 9 - 2x

f(g(x)) = (9 - 2x)² - (9 - 2x)

= 81 + 4x² - 36x - 9 + 2x

= 4x² - 36x + 2x + 81 - 9

= 4x² - 34x + 72

thus, option C is the correct answer

Answer 2

Answer: 4x^2 - 34r + 72

Explanation:

To find f(g(x)), we need to substitute the expression for g(x) into the function f(x).

First, let's find g(x) by substituting x into the function G(x):

G(x) = 9 - 2x

Now, we substitute G(x) into f(x) to find f(g(x)):

f(g(x)) = f(9 - 2x)

To find f(9 - 2x), we substitute 9 - 2x into the function f(x):

f(9 - 2x) = (9 - 2x)^2 - (9 - 2x)

Now, let's simplify the expression:

(9 - 2x)^2 = (9 - 2x)(9 - 2x) = 81 - 18x - 18x + 4x^2 = 81 - 36x + 4x^2

Substituting this back into the expression for f(g(x)):

f(g(x)) = (81 - 36x + 4x^2) - (9 - 2x)

Simplifying further:

f(g(x)) = 81 - 36x + 4x^2 - 9 + 2x = 4x^2 - 34x + 72

Therefore, f(g(x)) = 4x^2 - 34x + 72.

To summarize:

f(g(x)) = (9 - 2x)^2 - (9 - 2x)

f(g(x)) = 4x^2 - 34r + 72