Question

Please can I get an explanation, please!!

Answer 1

Find the inverse of

$y = \left( \dfrac 1 5 \right)^x$

For the inverse we swap x and y and solve for y.

$x = \left( \dfrac 1 5 \right)^y$

Taking logs base 1/5

$\log_{1/5} x = y$

$f^{-1}(x) = \log_{1/5} x$

Answer: Second Choice

Note: There's more simplification to do but we'll stop here.