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JEE MATHEMATICS MCQ: FUNCTIONS

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If b2−4ac=0  and  a>0{b^2} - 4ac = 0\;and\;a > 0 , then domian of the function f(x)=log⁡{(ax2+bx+c)(x+1)}f\left( x \right) = \log \left\{ {\left( {a{x^2} + bx + c} \right)\left( {x + 1} \right)} \right\} is
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Correct option: C
(−1,  ∞)−{−b2a}\left( { - 1,\;\infty } \right) - \left\{ { - \frac{b}{{2a}}} \right\}
Option C (\left( { - 1,\\;\infty } \right) - \left\\{ { - \frac{{b}}{{{{2a}}}}} \right\\}\left( { - 1,\\;\infty } \right) - \left\\{ { - \frac{{b}}{{{{2a}}}}} \right\\}) is correct because the domain requires the argument of the logarithm to be positive, and the quadratic has a repeated root.

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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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