JEE MATHEMATICS MCQ: FUNCTIONS

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Analyzing +4 | -1

The number of solutions of

\left[ {\sin x + \cos x} \right] = 3 + \left[ { - \sin x} \right] + \left[ { - \cos x} \right]

in the internal

\left[ {0,\;2\;\pi } \right]

is (where [.] denotes the greatest integer function)

View answer and explanation

Correct option: C

Infinite

Option C (Infinite) is correct because the two expressions are equivalent, leading to infinite solutions within the given interval.

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f:(-\infty, 2] \longrightarrow(-\infty, 4]

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f(g(x))=(\sin \sqrt{x})^2

f:\left( {2,\;3} \right) \to \left( {0,\;1} \right)

f\left( x \right) = x - \left[ x \right]

{f^{ - 1}}\left( x \right)

f: R \rightarrow R

f(x)=x^4

f(x)=(x+1)^2-1(x \geq-1)

S=\left\{x: f(x)=f^{-1}(x)\right\}