Question

Given the definitions of f(x) and g(x) below, find the value of (gof)(3).

f(x) = 3x - 9
g(x) = 3x² - 5x + 15

Answer 1

(gof)(3)=15

Explanation:

According to what I've learned that could be re-written as g[f(3)]

First, I would solve f(3), then proceed to get that value and plug it into the function g(x)

So the first step is to solve f(3)

Substitute all values of x for 3

f(3)=3(3)-9 Now just simplify

f(3)=0

Now that you have the value of f(3), you want to plug that value you obtained and plug it into g(x)

Substitute all x values for 0

g(0)=3(0)^2-5(0)+15 Now you simplify

g(0)=15

Answer 2

g(f(x)) = 27x² - 177x + 303

Explanation:

g(f(x)) = 3(3x - 9)² - 5(3x - 9) + 15

= 3(9x² - 54x + 81) - 15x + 45 + 15

= 27x² - 162x + 243 - 15x + 45 + 15

= 27x² - 177x + 303