Function composition given ( f o g)(x) = 2 + (x - 3) . (Please help >.<)

Question

a. Define Function of f(x) and g(x)

b. Define Function of

(g o f )(x)

Edited to make things simple

Answer 1

Function composition given ( f o g)(x) = 2 + (x - 3) .

**part a**

( f o g)(x) means that the function g(x) has been "plugged into" the overarching function f(x). I usually type ( f o g)(x) as f(g(x)) for this reason.

So you want to define g(x) as what has been "plugged into" the overall equation 2+(x-3)

This means that g(x) is most likely the function (x-3) as it appears to be what was plugged into the equation.

That means f(x)=2+x because f(g(x))=2+(x-3) so g(x) was replacing x as the second term.**

**part b**

Two summarize f(x)=2+x and g(x)=x-3. So (g o f)(x) AKA g(f(x)) must be g(x) (AKA x-3) with f(x) (AKA 2+x) plugged in for x. This means (g o f) = (2+x)-3 according to our previous definitions. This simplifies to (g o f) = 2+x-3 = x+2-3 =x+1. So (g o f)(x)= x+1