Question

Given the functions:

f(x) = x^2 - 1, g(x) = x/x + 2

Why is the followig the equation of (g o f)(x)

THe answer is x^2 - 1 / x^2 + 1

This is how I got the answer with someone's help:


Assume you forgot parenthese


g(x) = x / (x + 2)
g = x^2 - 1) / (x^2 - 1 + 2)
= (x^2 - 1)/(x^2 + 1)

Is there a simpler way to get the answer?
Thank you for any further assistance

Answer 1

I can't think of a better way to do it than your example.

g(x) = x/(x+2)
g[f(x)] = (x^2-1)/(x^2-1 +2)
= (x^2-1)/(x^2+1)