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Values of x satisfying \sin ^{-1}x>\sin ^{-1}x^2 is

Option: 1

[0,1]


Option: 2

(0,1)


Option: 3

(-1,0)


Option: 4

(-1,1)


Answers (1)

best_answer

We can see from the graph of sin-1x, we can see that it is an increasing function: higher input gives higher output

So if sin-1(p) > sin-1(q), then p > q

Now

\\\sin ^{-1}x>\sin ^{-1}x^2\\ x>x^2 \ \ \ \because \sin ^{-1}\text {is increasing }\\ x-x^2>0\\ x(1-x)>0\\x(x-1)<0)\\ x\in (0,1)

It also lies in the domain of both the given functions, so it is the answer

Posted by

Ajit Kumar Dubey

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