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

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

1 Answer
Jun 18, 2018

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)