Doubt from function

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For q38 is the answer {0,1} ?!

Sir answer is given (1) third option

I am sorry , i did a mistake there , wait I’ll post the correct solution for it .

Is the answer for cos inverse question is 1 and 1+ pie ?!

Yes sir 4 option is correct

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Sir can i post some more doubts from kvpy

Yes ! For sure

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Q38)
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@Achyut_2021 these questions are not from the chapter functions . So please create a new thread and post them with appropriate thread name :blush:

For tan inverse question is it onto function in the question? If yes then answer should be none of these i think
And if it is into function then option C i.e [1/4,infinity)

@Achyut_2021 are the answers mentioned in post#4 and post #11 correct ?

Yes sir

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Sir it is onto given

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So the answer should be none of these right ?!

Sir answer is given (1by4,infinity)

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For [1/4 , infinity) it must be into function

For onto function co domain = range and hence for range of tan inverse y to be [0,infinity) y must be all non negative value and hence
D=0 for x²+x+a and hence a=1/4

For into function range must can be a subset of co domain and hence y can be all or only few non negative values
And hence on condition id x²+x+a >= 0 for all x
And hence D<0 which will give x€ [1/4 , infinity)