Steps for composite functions

Question

show step by step

Answer 1

Alright, let's say we have f(x) = x² - 2x - 7 and you are asked for f(3).

 

f(3) = 3² - 2(3) - 7 = 9 - 6 - 7 = -4

 

Now, let's say g(x) = x³.

 

f(g(x)) = (x³)² - 2(x³) - 7 = x⁶ - 2x³ - 7

 

g(f(x)) = (x² - 2x - 7)³ = (x² - 2x - 7)(x² - 2x - 7)(x² - 2x - 7) = ...