What is the range of the function \(\rm f(x)=\dfrac{|x|}{x}, \ x \neq 0 \ ?\)

Question

Question

What is the range of the function \(\rm f(x)=\dfrac{|x|}{x}, \ x \neq 0 \ ?\)

Set of all real numbers
Set of all integers
{-1, 1}
{-1, 0, 1}

Answer 1

Concept:

\({\rm{f}}\left( {\rm{x}} \right) = \left| {\rm{x}} \right| = \left\{ {\begin{array}{*{20}{c}} { - x,\;\;x < 0}\\ {x,\;\;x \ge 0} \end{array}} \right.\)

Explanation:

Referring to the graph for the given function,

\(\rm f(x)=\dfrac{|x|}{x}, \ x \neq 0 \ \)

Here, x = 0 is not in the domain of f(x)

This can be re - written as,

\({\rm{f}}\left( {\rm{x}} \right)= \left\{ {\begin{array}{*{20}{c}} { - 1,\;\;x < 0}\\ {1,\;\;x > 0} \end{array}} \right.\)

So, referring to the graph for the given function,

F2 Vinanti Engineering 27.02.23 D3

You can see that there are only two outputs for all the values of x in the domain of f(x) so the range of the function f(x) will be {-1, 1}

Download Solution PDF

Question

What is the range of the function \(\rm f(x)=\dfrac{|x|}{x}, \ x \neq 0 \ ?\)

Answer (Detailed Solution Below)

Detailed Solution

More Range of a Function Questions

More Relations and Functions Questions

More Mathematics Questions