JEE MATHEMATICS MCQ: FUNCTIONS

1 Easy

1 of 1

Analyzing +4 | -1

f:(0, \pi) \rightarrow \mathbf{R}

is given by

f(x)=\sum\limits_{{k=1}}^n[1+\sin k x],[x]

denotes the greatest integer function, then the range of

f(x)

View answer and explanation

Correct option: C

\{n, n+1\}

Option C (

\left\{n, n+1\right\}

) is correct because the function f(x) can take two values, n when all

[\sin kx] = 0

, and n+1 when one of the

[\sin kx] = 1

and the rest are 0.

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\}