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JEE MATHEMATICS MCQ: FUNCTIONS

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The inverse of the function y=10x−10−x10x+10−xy = \frac{{{{10}^x} - {{10}^{ - x}}}}{{{{10}^x} + {{10}^{ - x}}}} is
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Correct option: A
12log⁡10(1+x1−x)\frac{1}{2}{\log _{10}}\left( {\frac{{1 + x}}{{1 - x}}} \right)
Option A is correct because the inverse function is found by swapping x and y, then solving for y, using componendo and dividendo and logarithmic properties.

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If f:(−∞,2]⟶(−∞,4]f:(-\infty, 2] \longrightarrow(-\infty, 4], where f(x)=x(4−x)f(x)=x(4-x), then f−1(x)f^{-1}(x) is given by: If g(f(x))=∣sin⁡x∣g(f(x))=|\sin x| and f(g(x))=(sin⁡x)2f(g(x))=(\sin \sqrt{x})^2, then Let f:(2,  3)→(0,  1)f:\left( {2,\;3} \right) \to \left( {0,\;1} \right) be defined by f(x)=x−[x]f\left( x \right) = x - \left[ x \right], then f−1(x){f^{ - 1}}\left( x \right) equals Let f:R→Rf: R \rightarrow R be defined as f(x)=x4f(x)=x^4, Choose the correct answer. Which of the following functions are odd functions Let f(x)=(x+1)2−1(x≥−1)f(x)=(x+1)^2-1(x \geq-1). Then the set S={x:f(x)=f−1(x)}S=\left\{x: f(x)=f^{-1}(x)\right\} contains
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