Question

Given the function `f(x) = 6(x+2)-3`, what is the inverse function when `x = 21`?

Answer 1

Inverse function: `f^-1(x) = 1/6x - 3/2`
When `x = 21, f(21) = 135`
When `f^-1(135) = 21`

Explanation:

Given: `f(x) = 6(x+2)-3 = 6x+12 - 3 = 6x + 9`
`f(21) = 135`

To find the inverse function first let `y = f(x)`:
`y = 6x + 9`

Next interchange `x` and `y`:
`x = 6y + 9`

Now solve for `y`:

`x - 9 = 6y`

`x/6 - 9/6 = y`

`y = 1/6x - 3/2`

The inverse function `(f^-1(x)) = 1/6x - 3/2`

`(f^-1(135)) = 1/6*135/1 - 3/2 = 21`