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Find range of f(x)=1-|x-2|

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Find range of f(x)=1-|x-2|

Posted by Prabh Fateh 6 years, 3 months ago

CBSE > Class 08 > Mathematics

1 answers

Sia ? 6 years, 3 months ago

According to the question, {tex}f ( x ) = 1 - | x + 2 |{/tex}
We can see that {tex}f(x){/tex}( x ) is defined for all x {tex}\in{/tex} R.
{tex}\therefore{/tex} Domain of f = R

As we know, {tex}0 \leq | x + 2 | < \infty{/tex}for all {tex}x \in R{/tex}
{tex}\Rightarrow - \infty < - | x + 2 | \leq 0{/tex} for all {tex}x \in R{/tex}
{tex}\Rightarrow - \infty < 1 - | x + 2 | \leq 1{/tex} for all {tex}x \in R.{/tex}
{tex}\Rightarrow - \infty < f ( x ) \leq 1{/tex} for all {tex}x \in R \Rightarrow f ( x ) \in ( - \infty , 1 ]{/tex}
{tex}\therefore{/tex} Range of {tex}f = ( - \infty , 1 ]{/tex}

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CBSE > Class 08 > Mathematics