# How do you find the inverse of f(x)= absx + 1?

Jul 26, 2018

${f}^{-} 1 \text{ does not exist}$.

#### Explanation:

Note that, for the function $f$ defined by $f \left(x\right) = | x | + 1 ,$

$f \left(- 1\right) = | - 1 | + 1 = 1 + 1 = 2 , \mathmr{and}$

$f \left(1\right) = | 1 | + 1 = 2$.

So, $f \left(- 1\right) = f \left(1\right)$.

Therefore, $f$ is not $1 - 1$.

We know that ${f}^{-} 1 \text{ exists "iff f" is 1-1 and onto}$.

Hence, for the given function $f$, its inverse does not exist.