Question

(vii) f(x)= -|x-2| find range and domain
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Answer 1

We're given the function,

$\longrightarrow f(x)=-|x-2|$

We need to find its domain and range.

Since no domain restriction is seen in the function, the domain is none other than the set of all real numbers.

$\longrightarrow\underline{\underline{x\in\mathbb{R}}}$

Since $|x|\geq0$ for every real number $x,$ we have,

$\longrightarrow|x-2|\geq0$

Multiplying by -1, (note the symbol change)

$\longrightarrow-|x-2|\leq0$

$\longrightarrow-|x-2|\in\left(-\infty,\ 0\right]$

Hence the range is,

$\longrightarrow\underline{\underline{f(x)\in\left(-\infty,\ 0\right]}}$