Question

Find g^−1(x) when g(x)=3/5x−9.

Answer 1

Answer:

$g^-^1(x) = \frac{5}{3} x + 15$

Step-by-step explanation:

Based on the function $g(x)$, we have to find the function $g^-^1(x)$. 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 $g(x)$ is the "y" of the function):

$g(x) = \frac{3}{5}x-9\\x = \frac{3}{5}y-9$

2) Now, with the new equation, isolate y. Whatever the end result is, is the inverse of the original function, and therefore $g^-^1(x)$:

$x = \frac{3}{5} y-9\\x + 9 = \frac{3}{5} y\\\frac{5}{3}x + 15 = y \\g^-^1(x) = \frac{5}{3} x + 15$

Thus, $g^-^1(x) = \frac{5}{3} x + 15$.