Question

3) Given the following functions,

f(x)=x+2 and g(x) = 3x - 4


3A) Find (fog)(-1/3)




3B) Find (gof)(x)




3C) Determine if f(x) and g(x) are inverses. Explain your result in a full sentence.

Answer 1

Part A

`g(-1/3)=3(-1/3)-4=-5\\\\f(g(-1/3))=f(-5)=-5+2=\boxed{-3}`

Part B

`g(f(x))=g(x+2)=3(x+2)-4=3x+6-4=\boxed{3x+2}`

Part C

Since
`g(f(x)) \\eq x`,
`g(x)` and
`f(x)` are not inverses.