Question

Given the functionf(x)=0.5(3)^x, what is value of f-1(7)

Answer 1

Ok, a fun hack

if f⁻¹(a)=b then f(b)=a

so if f⁻¹(7)=b then f(b)=7

to find b, find x such that f(x)=7


7=0.5(3)^x
times both sides by 2 (or divide both sides by 0.5)
14=3^x
take log₃ of both sides
$log_3(14)=x$

$f^{-1}(7)=log_3(13)$