# How do you find the inverse of #f(x) = 5 sin^{-1}( frac{2}{x-3} )#?

##### 1 Answer

Well... you kind of can and cannot....

#### Explanation:

I will explain the method used for finding the inverse function but keep in mind that the answer is not an actual inverse function. The reason there is no inverse function is because

When finding the inverse of a function it helps to think of functions in terms of x and y.

where f is a function stating that y is equal to the right hand side.

Then you switch the x's and y's and write it as the inverse function for x.

However, to get the inverse function for y, we must rearrange the equation to get y on the left hand side along with

Therefore, we find the inverse function to be:

But remember that for this to be an inverse function there must be a restricted domain making the original function a one-to-one function. A one-to-one function is a function where for each x there is only one value of y and vice versa