Question

Question 1
Given: f(x)=x2-1 and g(x) = 2x-5
Find: (gof)(x)

Answer 1

`(g\circ f)(x)=2x^2-7`

Explanation:

So we have the two functions:

`f(x)=x^2-1\text{ and } g(x)=2x-5`

And we want to find:

`(g\circ f)(x)`

This is the same as:

`=g(f(x))`

So, substitute f(x) into g(x). Thus:

`g(x)=2x-5\\g(f(x))=2(x^2-1)-5`

Distribute the 2:

`g(f(x))=2x^2-2-5`

Subtract:

`g(f(x))=2x^2-7`

Therefore:

`(g\circ f)(x)=2x^2-7`

And we're done!