SOLUTION: please explain: Determine whether f(x)=6/(x+5) is one-to-one. If it is one-to-one, find a formula for the inverse.

Question 1140384: please explain:
Determine whether f(x)=6/(x+5) is one-to-one. If it is one-to-one, find a formula for the inverse.
Answer by MathLover1(20849) (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 value ONLY has ONE unique value mapping to it.
In this case, we're assuming that and are two different values that map to the same }value (but as you'll see, they are in fact the same value)

Start with the given equation
...divide by
.......cross multiply
.......cancel

So we've shown that if , then . This means that is one-to-one.
now, find a formula for the inverse:
........recall that
.......swap and
.........solve for

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