Precalc Inverse function

Question

Find the inverse function of f.

f(x) = log₆(x − 1)

f ⁻¹(x) =

Answer 1

y = log base 6 (x-1)

to find inverse switch x and y

then solve for new y= f^-1(x)

x = log base 6 (y-1)

rewrite in exponential form

6^x = y-1

y = 1 +6^x = f^-1(x)

Answer 2