Inverse of Absolute Value Function

Algebra Level 3

Consider the function $f: [ -1, \infty) \rightarrow \mathbb{R}$ , given by $f(x)=|x+1|+1$ .

Which of the following must be in the domain of the inverse function $f^{-1}(x)$ ?

I : $-1$ .
II : $0$ .
III : $1$ .

Notation : $| \cdot |$ denotes the absolute value function .

II and III only I only III only None I and II only

1 solution

James Dohm
Jul 18, 2016

The range of $f(x)$ is the same as the domain of $f^{-1}(x)$ . Because the range of $f(x)$ is all real numbers greater than or equal to one, only III is in the domain of $f^{-1}(x)$ .

Inverse of Absolute Value Function

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