Question

Find the range :

$f\left(x\right)=|x-3|$

• A. $[0,\infty )$
• B. $(-\infty ,\infty )$
• C. $[0,1]$
• D. None of these

Answer 1

The correct option is A $[0,\infty )$

$f\left(x\right)=|x-3|$

$f\left(x\right)$ is defined for all $x\in R$. Therefore, Domain (f) = R

Since, $|x-3|>0$ for all $x\in R$

Therefore, $0\le |x-3|<\infty$ for all $x\in R$

$0\le f\left(x\right)<\infty$ for all $x\in R$

$f\left(x\right)\in [0,\infty )$ for all $x\in R$

Hence, Range (f) = $[0,\infty )$