Question

If f(x) = 5x + 5, then f-'(x)=

Answer 1

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

Step-by-step explanation

I believe the question means:

`f^(-1)(x)`

This is called the Inverse function.

To do this, first we replace f(x) with y:

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

Now, we replace every y with x and vice versa:

`*\text{ = 5y + 5}`

Now, make y subject of formula:

`\begin{gathered} \text{ x = 5y + 5} \\ x\text{ - 5 = 5y} \\ 5y\text{ = x - 5} \\ (5y)/(5)=\text{ }(x)/(5)-\text{ }(5)/(5) \\ y\text{ = }(x)/(5)\text{ -1} \\ f^(-1)(x)\text{ = }(x)/(5)\text{ - 1} \end{gathered}`

That is the inverse function