Question

For each non-zero real number $x$, let $f\left(x\right)=\frac{x}{|x|}$. The range of $f$ is.

• A. A null set
• B. A set consisting of only one element
• C. A set consisting of two element
• D. A set consisting of infinitely many elements

Answer 1

The correct option is C A set consisting of two element

For negative number $(x<0),f\left(x\right)=\frac{x}{-x}=-1$

For positive number $(x>0),f\left(x\right)=\frac{x}{x}=1$

$\therefore$ Range of $f$ is a set consisting of two elements.