Question

Find f(g(x)) and g(f(x)) and determine whether the pair of functions f and g are inverses of each other.

f(x)=6x+5 and g(x)= x-5/6
a. f(g(x))= (Simplify your answer.)
b. g(f(x))= (Simplify your answer.)

Answer 1

Part a

`f(g(x))=6\left(x-(5)/(6))+5=6x-5+5=6x`

Part b

`g(f(x))=g(6x+5)=(6x+5)-(5)/(6)=6x+(25)/(6)`

Therefore, the functions are not inverses of each other since
`(f(g(x)) \\eq x`.