Question

108. Find the inverse g for each function f.
e. f(x) = log(2x+ 3)

Answer 1

`x=(10^(x)-3)/(2)`

Explanation:

A logarithm is the inverse of an exponent, that is:

`y=log_(b)(x)\\b^(y)=x`

Using this property we can solve x and get the inverse function:

`f(x)=log(2x+3)\\\\y=log(2x+3)\\\\10^(y)=2x+3\\\\x=(10^(y)-3)/(2)\\\\y=(10^(x)-3)/(2)\\\\\\g(x)=f^(-1)(x)=(10^(x)-3)/(2)`