If $\alpha \leq \log _{\sqrt{5}}[\sqrt{2}(\sin x-\cos x)+3] \leq \beta$ then

JEE MATHEMATICS MCQ: FUNCTIONS

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Application +4 | -1

\alpha \leq \log _{\sqrt{5}}[\sqrt{2}(\sin x-\cos x)+3] \leq \beta

then

View answer and explanation

Correct option: C

\alpha=0, \beta=2

The correct answer is C (

\alpha=0, \beta=2

) because by finding the range of

\sin x - \cos x

and then the range of the entire expression, we can determine the bounds of the logarithm.

Practice All Chapter MCQs →

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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\}