Question

What is the inverse of f^-1(x) =5x + 4

Answer 1

`f(x)\text{ = }(x)/(5)\text{ - }(4)/(5)`

Step-by-step explanation

We have to find the inverse of:

`f^(-1)(x)\text{ = 5x + 4}`

First, replace f^(-1) (x) with x and replace x with y:

`x\text{ = 5y + 4}`

Now, make y the subject of the formula:

`\begin{gathered} x\text{ - 4 = 5y} \\ \text{Divide through by 5:} \\ y\text{ = }\frac{x\text{ - 4}}{5}\text{ } \\ y\text{ = }(x)/(5)\text{ - }(4)/(5) \end{gathered}`

Now, replace y with f(x):

`f(x)\text{ = }(x)/(5)\text{ - }(4)/(5)`

That is the inverse.

Note: The inverse of f^-1(x) is f(x).