Question

Determining if two functions are inverses. 15 pts

Answer 1

The answer is the first one because u could see how it is but I think I try my best

Answer 2

An inverse function
`f^(-1)` is such that

`f\left(f^(-1)(x)\right) = f^(-1)(f(x)) = x`

(a) Given
`f(x) = x-3` and
`g(x) = x+3`, we have

`f(g(x)) = f(x+3) = (x+3)-3 = x`

and

`g(f(x)) = g(x-3) = (x-3)+3 = x`

so
`f` and
`g` are indeed inverses of one another.

(b) Given
`f(x)=\frac1{4x}` and
`g(x)=-\frac1{4x}`, we have

`f(g(x)) = f\left(-\frac1{4x}\right) = \frac1{4\left(-\frac1{4x}\right)} = -\frac1{\frac1x} = -x \\eq x`

so
`f` and
`g` are not inverses of one another.