If A - x - R - - 4 - x - 3 and f x - sin x - x then f A -

The correct option is A [ √( 3 )/ 2 π/ 3 , 1 /√( 2 ) π/ 4 ] f ( x ) = sin x x Which is decreasing function in #160; #160; [ π/ 4 , π/ ...

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Byju's Answer

Standard XII

Mathematics

Definition of Function

If A = x ∈ ...

Question

If $A = {x \in R / \frac{π}{4} \leq x \leq \frac{π}{3}}$ and $f (x) = sin x - x$ then $f (A) =$

[\frac{\sqrt{3}}{2} - \frac{π}{3}, \frac{1}{\sqrt{2}} - \frac{π}{4}]

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[- \frac{1}{\sqrt{2}} - \frac{π}{4}, \frac{\sqrt{3}}{2} - \frac{π}{3}]

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[- \frac{π}{3}, \frac{- π}{4}]

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[\frac{π}{4}, \frac{π}{3}]

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Solution

The correct option is A $[\frac{\sqrt{3}}{2} - \frac{π}{3}, \frac{1}{\sqrt{2}} - \frac{π}{4}]$
$f (x) = sin x - x$
Which is decreasing function in $[\frac{π}{4}, \frac{π}{3}]$
$∴ \frac{π}{4} \leq x \leq \frac{π}{3}$
$\Rightarrow f (\frac{π}{4}) \geq f (x) \geq f (\frac{π}{3})$
$\Rightarrow \frac{1}{\sqrt{2}} - \frac{π}{4} \geq f (x) \geq \frac{\sqrt{3}}{2} - \frac{π}{3}$
$f (A) \in [\frac{\sqrt{3}}{2} - \frac{π}{3}, \frac{1}{\sqrt{2}} - \frac{π}{4}]$

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If A={x∈R/π4≤x≤π3} and f(x)=sinx−x then f(A)=

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