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JEE MATHEMATICS MCQ: FUNCTIONS

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Application +4 | -1
If the function f:[1,  ∞)→[1,  ∞)f:\left[ {1,\;\infty } \right) \to \left[ {1,\;\infty } \right) is defined by f(x)=2x(x−1),  f\left( x \right) = {2^{x\left( {x - 1} \right)}},\; then f−1(x){f^{ - 1}}\left( x \right) is
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Correct option: B
12(1+1+4log⁡2y)\frac{1}{2}\left( {1 + \sqrt {1 + 4{{\log }_2}y} } \right)
Option B (12(1+1+4log⁡2y)\frac{1}{2}\left( {1 + \sqrt {1 + 4{{\log }_2}y} } \right)) is correct because it is the inverse function obtained by solving for x in terms of y and considering the domain of the original function.

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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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