Answer:
[tex]g^-^1(x) = \frac{5}{3} x + 15[/tex]
Step-by-step explanation:
Based on the function [tex]g(x)[/tex], we have to find the function [tex]g^-^1(x)[/tex]. This is known as finding the inverse of a function.
1) To find the inverse of a function, first take the original function and switch the places of the x and y variables like so (the [tex]g(x)[/tex] is the "y" of the function):
[tex]g(x) = \frac{3}{5}x-9\\x = \frac{3}{5}y-9[/tex]
2) Now, with the new equation, isolate y. Whatever the end result is, is the inverse of the original function, and therefore [tex]g^-^1(x)[/tex]:
[tex]x = \frac{3}{5} y-9\\x + 9 = \frac{3}{5} y\\\frac{5}{3}x + 15 = y \\g^-^1(x) = \frac{5}{3} x + 15[/tex]
Thus, [tex]g^-^1(x) = \frac{5}{3} x + 15[/tex].
