# How do you write the inverse function for f(x)=1/2x+4?

Nov 18, 2016

The answer is ${f}^{- 1} \left(x\right) = 2 \left(x - 4\right)$

#### Explanation:

Let $y = \frac{x}{2} + 4$

Then, $\frac{x}{2} = y - 4$

$y = 2 \left(y - 4\right)$

So, ${f}^{- 1} \left(x\right) = 2 \left(x - 4\right)$

Verification

$f \left({f}^{- 1} \left(x\right)\right) = f \left(2 \left(x - 4\right)\right) = \frac{1}{2} \cdot 2 \left(x - 4\right) + 4 = x$