Algebra 2 question, only need an answer

Question

Let f(x)=x^2+2x-3 and let g(x)=2x-1. Then find (g o f)(a)

Answer 1

Composing functions g and f, read it as g(f(a)), or "g of f of a". See the parentheses? You do this from the inside out.

 

The parameter of f(x) [the inner function] is "x". You are "passing" an "a" to function f, so for every "x" in f's definition, substitute "a":

 

f(x) = x² + 2x - 3 TO

f(a) = a² + 2a - 3

 

Now, here is the tricky part: you are passing that "a² + 2a - 3" to function g. The parameter of g(x) is "x", so for every "x" in g's definition, substitute "a² + 2a - 3":

 

g(x) = 2x - 1 TO

g(a² + 2a - 3) = 2(a² + 2a - 3) - 1 = 2a² + 4a - 6 - 1 = 2a² + 4a - 7

 

Therefore, g(f(a)), or (g o f)(a) = 2a² + 4a - 7.