# How do you find #f^-1(x)# given #f(x)=2x+7#?

##### 2 Answers

#### Explanation:

Given:

Let y=f(x)

Expressing x in terms of y gives us the inverse of x

Thus,

The

#### Explanation:

There are a couple of ways to look at function inverses. An inverse of anything allows you to 'undo' whatever you started with. So, if you tie your shoe, it's not there forever - you can always untie it.

We have many inverse functions in math, such as square root is the inverse of squaring a number, etc.

Finding the inverse also reflects the graph across the line y = x.

There are 3 steps to finding an inverse:

1) change notation

So, y = 2x + 7

2) Exchange the x & y variables. Note this is what accomplishes that reflection across the line y = x

So, x = 2y + 7

3) Since *x* is the dependent variable and *y* is the independent variable and it is always a zillion times easier to solve a problem in *y =* form, solve the equation for *y.*

First subtract 7 from both sides

x - 7 = 2y

Then divide by 2