SOLUTION: Can someone answer this for me? a) Show that the function f(x) = x/x-4 is a ont-to-one function? b) find the inverse of the function. Thank you.

Question 169138: Can someone answer this for me?
a) Show that the function f(x) = x/x-4 is a ont-to-one function?
b) find the inverse of the function.
Thank you.

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
In order to show that is one-to-one, we need to show that if , then .

In other words, we need to show that each y value ONLY has ONE unique x value mapping to it. In this case, we're assuming that and are two different values that map to the same y value (but as you'll see, they are in fact the same value)

Start with the given equation

Plug in the function

Cross multiply

Distribute

Rearrange the terms.

Subtract from both sides. Notice how they cancel out on both sides.

Simplify

Divide both sides by -4. Once again, they cancel out on both sides.

Simplify

So we've just shown that if , then . This means that is one-to-one.

================================================

Start with the given function

Replace f(x) with y

Switch x and y. The goal is to solve for y

Multiply both sides by

Distribute

Subtract from both sides.

Factor out the GCF y

Divide both sides by to isolate y

So the answer is which means that the inverse function is

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