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Standard XII

Mathematics

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The range of ...

Question

The range of the function : $f (x) = | x - 3 |$

π

-2,0]

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[0,

\infty

)

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[ 0,

π

+4]

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[ 0,

π

+2]

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Solution

The correct option is B [0, $\infty$ )
We have, $f (x) = | x - 3 |$
Clearly, f(x) is defined for all $x \in R$ . Therefore, Domain (f) = R
Since, $| x - 3 | > 0$ for all $x \in R$
Therefore,
$0 \leq | x - 3 | < \infty$ for all $x \in R$
$0 \leq f (x) < \infty$ for all $x \in R$
$f (x) \in [0, \infty)$ for all $x \in R$
Hence, Range (f) = $[0, \infty)$ .

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The range of the function : f(x)=|x−3|

The correct option is B [0,∞)We have, f(x)=|x−3|Clearly, f(x) is defined for all x∈R. Therefore, Domain (f) = RSince, |x−3|>0 for all x∈RTherefore,0≤|x−3|<∞ for all x∈R0≤f(x)<∞ for all x∈Rf(x)∈[0,∞) for all x∈RHence, Range (f) = [0,∞).

The range of the function : $f (x) = | x - 3 |$