Question

Question #b6e1b

Answer 1

Yes. See explanation.

Explanation:

If `f(x)=1/2x+1`, then we know that `f(x)` is increasing with a constant slope of `1/2`. That means that `f(x)` is a one-to-one function, so it has an inverse that is a function.

You could also just find the inverse in this case. If `g(x)=f^-1(x)`:

`f(g(x))=1/2g(x)+1=x`

Solving for `g(x)`:

`1/2g(x)+1=x`

subtract 1 from each side:

`1/2g(x)=x-1`

multiply through by 2:
`g(x)=2x-2`