Question

use f(x)=x+2 and g(x)=3x+1 to find specified function (g o f)^-1

Answer 1

For this it would appear that you need to compose the inverse of g(f(x))

Answer 2

(g o f)^-1=g^-1(f(x))
1. => Find g^-1(x):
g(x)=3x+1
So
g(g^-1(x))=3*g^-1(x)+1
We know for any function g(g^-1(x))=x
.: x=3*g^-1(x)+1
Solving for g^-1 using elementary algebra:
g^-1(x)=(x-1)/3
Substituting f(x) into x:
g^-1(f(x))=(f(x)+1)/3
...=(x+2+1)/3
...=(x/3)+1
.:(g o f)^-1=(x/3)+1