Question

Find the inverse of the following function:(x) = 5x + 4Answer 5 Points-'(x) =

Answer 1

Hello there. To solve this question, we'll have to remember some properties about inverse functions.

First, an inverse function is the same as reflecting the function on the function f(x) = x, that is called the identity for inverse functions.

First, graphing the function:

`f(x)=5x^3+4`

We have

In order to reflect this function, we have to change x by y and solve for y i this case.

Think of this as changing coordinates for which [x y]^T goes to [y x]^T and we want to find the image of this function in this new coordinates.

Changing the variables, we get

`x=5y^3+4`

Subtract 4 on both sides of the equation

`x-4=5y^3`

Divide both sides of the equation by a factor of 5

`y^3=(x-4)/(5)`

Take the cuberoot on both sides of the equation

`y=\sqrt[3]{(x-4)/(5)}`

This is the inverse of this function, that we write as

`f^(-1)(x)=\sqrt[3]{(x-4)/(5)}`

And its graph is as follows (complementing the first image):