Answer
$h^{-1}(t) = 0.2^{t}$
Work Step by Step
$h(t) = \log_{0.2} t$
Let $h(t) = y$
$y = \log_{0.2} t$
Swap the variables $t$ and $y$ and then solve for $y$ to find the inverse:
$t = \log_{0.2} y$
$y = 0.2^{t}$
$h^{-1}(t) = 0.2^{t}$
You can help us out by revising, improving and updating this answer.
Update this answerAfter you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.