The range of the function f(x)=tan−1[x], −π4≤x≤π4 where [. ] denotes the greatest integer function

f(x)=tan−1[x]If −π4≤ x≤ π4⇒ −0.78≤x≤0.78∴ [x]={−1, 0}Range ={f(−1), f(0)}={ Tan−1(−1), tan−1(0)}⇒ {−π4, 0}

The range of the function f(x)=tan−1[x], −π4≤x≤π4 where [. ] denotes the greatest integer function

f(x)=tan−1[x]If −π4≤ x≤ π4⇒ −0.78≤x≤0.78∴ [x]={−1, 0}Range ={f(−1), f(0)}={ Tan−1(−1), tan−1(0)}⇒ {−π4, 0}

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$T h e r a n g e o f t h e f u n c t i o n f (x) = \tan^{- 1} [x], - \frac{π}{4} \leq x \leq \frac{π}{4} w h e r e [.] d e n o t e s t h e g r e a t e s t int e g e r f u n c t i o n$

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${- \frac{π}{4}, 0}$

$[- \frac{π}{4}, \frac{π}{4}]$

${\pm \frac{π}{4}}$

${- 1, 0}$

answer is A.

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Detailed Solution

$\begin{array}{l} f (x) = \tan^{- 1} [x] \\ I f \frac{- π}{4} \leq x \leq \frac{π}{4} \\ \Rightarrow - 0.78 \leq x \leq 0.78 \\ ∴ [x] = {- 1, 0} \\ R a n g e = {f (- 1), f (0)} = {{Tan}^{- 1} (- 1), \tan^{- 1} (0)} \\ \Rightarrow {- \frac{π}{4}, 0} \end{array}$