JEE MATHEMATICS MCQ: FUNCTIONS

1 Easy

1 of 1

Analyzing +4 | -1

f: \boldsymbol{R} \rightarrow \boldsymbol{R}

given by

f(x)=a x+\sin x+a

, then

f

is one-one and onto for all

View answer and explanation

Correct option: B

a \in \mathbf{R}-[-1,1]

Option B (

a \in \mathbf{R}-[-1,1]

) is correct because for f(x) to be one-one and onto, it must be strictly monotonic, which requires that

f'(x) = a + \cos x

be either always positive or always negative, implying

|a| > 1

More Questions from FUNCTIONS

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

f(x)=x(4-x)

f^{-1}(x)

g(f(x))=|\sin x|

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\}