# How do you find the inverse of # f(x) = ln(4 - 7x) + ln(-7 - 5x)#?

##### 1 Answer

There is no inverse, because the quadratic formula yields two equations that returns two values for any given x and an inverse must not do this.

#### Explanation:

Let

Substitute

Use the property of inverses

Use the identity

Use the inverse of the natural logarithm on both sides:

Use the F.O.I.L. method to perform the multiplication:

This is a quadratic.

At this point, we must declare that there is no inverse, because the quadratic formula yields two equations that returns two values for any given x and an inverse must not do this.

Let's proceed so that you can see the issue

Use the quadratic formula,

AND

This is contrary to the purpose of an inverse function.

The purpose of an inverse function is, for any