Question

How do you find the inverse of `f(x)=log_3(x-4)-2`?

Answer 1

`barf(x) = 3^(x+2)+4`

Explanation:

Let `barf(x)` be the inverse of `f(x)=log_3(x-4)-2`

By definition of an inverse:
`color(white)("XXX")f(barf(x))=x`

Therefore
`color(white)("XXX")f(barf(x)) = log_3(barf(x)-4)-2 = x`

`color(white)("XXX")log_3(barf(x)-4) = x+2`

and since `(log_b a = c) hArr (b^c=a)`
`color(white)("XXX")3^(x+2) = barf(x)-4`

`color(white)("XXX")barf(x) = 3^(x+2) + 4`