Answer:
A. [tex]f(x)=\frac{12}{x}-18[/tex] and [tex]g(x) = \frac{12}{x+18}[/tex]
Step-by-step explanation:
For find the inverse of a funtion we have to solve for x in the equation:
[tex]f(x)=\frac{12}{x}-18[/tex]
First, replace f(x) to y and solve for x as:
[tex]y=\frac{12}{x}-18[/tex]
[tex]y+18=\frac{12}{x}[/tex]
[tex]x(y+18)= 12[/tex]
[tex]x = \frac{12}{y+18}[/tex]
and finally we interchange y and x as:
[tex]y = \frac{12}{x+18}[/tex]
and replace y by g(x):
[tex]g(x) = \frac{12}{x+18}[/tex]
So, the inverse of the function [tex]f(x)=\frac{12}{x}-18[/tex] is [tex]g(x) = \frac{12}{x+18}[/tex]
