Answer:
The first choice, [tex]y = \log_6x[/tex].
Step-by-step explanation:
[tex]\log_b{x}[/tex] is logarithm of [tex]x[/tex] to the base [tex]b[/tex] (the base must be positive.) Raising the base [tex]b[/tex] to a power of [tex]\log_b{x}[/tex] would give [tex]x[/tex]. In other words, [tex]b^{\log_b{x}} = x[/tex].
If [tex]f^{-1}[/tex] is indeed the inverse of the function [tex]f[/tex], then [tex]f^{-1}(f(x)) = x[/tex]. Apply this property of inverse functions to check each option. By the logarithm property (in this case if [tex]b = 6[/tex],) [tex]6^{\log_6{x} = x[/tex]. In other words, the first choice is indeed the inverse of [tex]f(x) = 6^x[/tex].
