Question

Given f(x)=11^x, what is f^-1(x)?

Answer 1

The first one

`log_(11) \: (x)`

Explanation:

f(x) = 11^x

Here are the steps to find the inverse of a function:

1. Let f(x)=y

2. Make x the subject of formula.

3. Replace y by x.

`11 {}^(x) = y \\ \: log(11 {}^(x) ) = log(y) \\ x log(11) = log(y) \\ x = ( log(y) )/( log(11) ) = log_(11)(y) \\ f {}^( - 1) (x) = log_(11)(x)`