Find the domain and range of the function f(x)=1-|x-2| - Vidyadip

Question

Find the domain and range of the function $f(x)=1-|x-2|$

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Answer

According to the question, $f(x)=1-|x-2|$
We observe that $f(x)$ is defined for all $x \in R$. Therefore, Domain $(f)=R$
$\therefore 0 \leq|x-2|<\infty$ for all $x \in R$
$\Rightarrow-\infty<-|x-2| \leq 0$ for all $x \in R$
$\Rightarrow-\infty<1-|x-2| \leq 1$ for all $x \in R$
$\Rightarrow-\infty < f(x) \leq 1$ for all $x \in R$
$\therefore$ Range $(f)=(-\infty, 1]$

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