Question

Given the definitions of f(x) and g(x) below, find the value of (gof)(9).f(x) = 2 – 14g() = 2?+ 2a + 12

Answer 1

(g o f)(9) = 27

Step-by-step explanation

We are given that

f(x) = x - 14

g(x) = x² + 2x + 12

We are then told to find (g o f)(9)

(g o f)(x) refers to writing g(x), but instead of x, we will replace x by f(x).

That is,

(g o f)(x)

= g(f(x))

= [f(x)]² + 2 [f(x)] + 12

= (x - 14)² + 2 (x - 14) + 12

= x² - 28x + 196 + 2x - 28 + 12

= x² - 26x + 180

So, for (g o f) (9), we will substitute 9 for x

(g o f)(x) = x² - 26x + 180

(g o f)(9) = 9² - 26(9) + 180 = 81 - 234 + 180 = 27

Hope this Helps!!!