Question

Find the range of :

$f\left(x\right)=1-|x-2|$

• A. $\left(-\infty ,1\right]$
• B. $\left(0,\infty \right)$
• C. $\left(-\infty ,\infty \right)$
• D. None of the above

Answer 1

Answer: (A)

$\left(-\infty ,1\right]$

$f\left(x\right)=1-|x-2|$

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

Since, $0\le |x-2|<\infty$ for all $x\in R$

Therefore,

$-\infty <-|x-2|\le 0$ for all $x\in R$

$-\infty <1-|x-2|\le 1$ for all $x\in R$

$-\infty <f\left(x\right)\le 1$ for all $x\in R$

$f\left(x\right)\in (-\infty ,1]$