Question

How do you find the inverse of `log _(1/2) (x+4)=y`?

Answer 1

`f^-1(x)=2^-x-4`

Explanation:

Given `f(x)=log_(1/2)(x+4)`.
By definition, if `f(x)=y` then, `f^{-1}(y)=x`

Now, I'm sure you're familiar with log identities and functions and also a bit of law of indices, so
`y=log_(1/2)(x+4)implies(1/2)^y=x+4\implies2^-y-4=x`
We have `f^-1(y)=x`
So that means `f^-1(y)=2^-y-4`

Replace `y` with `x` and there you have it.