### 2) Inverse functions

An **inverse function** is a second function which undoes the work of the ﬁrst one. In this unit we describe two methods for ﬁnding inverse functions, and we also explain that the domain of a function may need to be restricted before an inverse function can exist.

**Question 1**

If , find

First, rearrange in terms of:

Remember to change *y *back to *x* when you’re writing your answer:

, therefore

**Question 2**

Find the inverse of .

To ﬁnd the inverse of *f(x)*, we swap the *x* and *y* values which represent the inputs and outputs. To ﬁnd the inverse function we now make *y *the subject.

Therefore,

Now use the same method to solve this question.

(a) for

(b) for

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