Find the number of solutions for the equationtan(tan−1(x))=x2 in the interval (0,∞).
A
1
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B
2
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C
3
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Solution
The correct option is A 1 This question is best solved graphically. Lets draw the functions y=tan(tan−1(x)) and y=x2and see the number of intersections. Number of intersections will be the number of solutions. We know tan(tan−1(x))=x for all x. In the interval (0,∞)there is only one point of intersection which is (1, 1).