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NDA 2023

Exam: NDA
Year: 2023
Subject: Mathematics
Chapter: Functions

NDA 2023 · Mathematics · Functions

What is the range of the function f(x)=x+|x| if the domain is the...

What is the range of the function

f(x)=x+|x|

if the domain is the set of real numbers?

Options

A $(0, \infty)$
B $[0, \infty)$
C $(-\infty, \infty)$
D $[1, \infty)$

Correct answer

B. $[0, \infty)$

Step-by-step solution

f(x)=x+|x|

when

x < 0, f(x)=x-x=0

when

x \geq 0, f(x)=x+x=2 x\therefore \quad f(x) \in(0, \infty)

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