Question

What is the inverse of the given function? f (x) = −6^x

`f(x)=-6^x`
`f^-1(x)=?`

Answer 1

`y=log_6 (-x)`

Explanation:

*I'm assuming that the base is `-6^x` and not `(-6)^x`.

If it is the first: switch the variables so you have `-x=6^y`
Next, take the log base 6 of both sides `log_6 -x= log_6 (6^y)`
One logarithm law states that `log_6 (6^y)` can be written as `y*log_6 6` and `log_6 6=1` so just `y`.
Finally, we have `y=log_6 (-x)`