Question

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

Answer 1

Answer:

$x=\frac{10^{x}-3}{2}$

Step-by-step 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:

$f(x)=log(2x+3)\\\\y=log(2x+3)\\\\10^{y}=2x+3\\\\x=\frac{10^{y}-3}{2}\\\\y=\frac{10^{x}-3}{2}\\\\\\g(x)=f^{-1}(x)=\frac{10^{x}-3}{2}$