Find the inverse of
[tex] y = \left( \dfrac 1 5 \right)^x [/tex]
For the inverse we swap x and y and solve for y.
[tex] x = \left( \dfrac 1 5 \right)^y [/tex]
Taking logs base 1/5
[tex] \log_{1/5} x = y[/tex]
[tex]f^{-1}(x) = \log_{1/5} x[/tex]
Answer: Second Choice
Note: There's more simplification to do but we'll stop here.
