JEE MATHEMATICS MCQ: FUNCTIONS

1 Hard

1 of 1

Analyzing +4 | -1

The domain of the function

e^x+\operatorname{Sin}^{-1}\left(\frac{x}{2}-1\right)+\log (\sqrt{x-[x]})

where

[x]

is the integral part of

x

View answer and explanation

Correct option: D

(0,4)-\{1,2,3\}

Option D (

(0,4)-\{1,2,3\}

) is correct because it represents the intersection of the domains of all three terms in the function.

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

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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\}