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

${f}^{-} 1 \left(x\right) = \frac{1}{2} \left(y - 7\right)$

#### Explanation:

Given:
$f \left(x\right) = 2 x + 7$

Let y=f(x)

$y = 2 x + 7$

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

$y - 7 = 2 x$

$2 x = y - 7$

$x = \frac{1}{2} \left(y - 7\right)$

Thus,

${f}^{-} 1 \left(x\right) = \frac{1}{2} \left(y - 7\right)$

Mar 3, 2018

The ${f}^{- 1}$ notation indicates you need to find the inverse of the function

#### 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 $f \left(x\right) =$ to y =

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

$y = \frac{x - 7}{2}$