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Draw the graph of f(x) =cot^(-1)((2-|x|)...

Draw the graph of `f(x) =cot^(-1)((2-|x|)/(2+|x|))`.

A

`f(x)` is bijective

B

`f(x)` is continuous and differentiable in `(-2,2)`

C

`f(x)` is even function

D

`underset(xto(2)/(sqrt(3)))(lim)f(x)=(5pi)/(12)`

Text Solution

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The correct Answer is:
B, C, D
`f(x)=(pi)/(2)-tan^(-1)((1-(|x|)/(2))/(1+(|x|)/(2)))=(pi)/(4)+tan^(-1)((|x|)/(2))`
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