Question

Find g^−1(x) when g(x)=3/5x−9.

Answer 1

`g^-^1(x) = (5)/(3) x + 15`

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) = (3)/(5)x-9\\x = (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 = (3)/(5) y-9\\x + 9 = (3)/(5) y\\(5)/(3)x + 15 = y \\g^-^1(x) = (5)/(3) x + 15`

Thus,
`g^-^1(x) = (5)/(3) x + 15`.