WB JEE 2011 | Functions Question 10 | Mathematics

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WB JEE 2011

MCQ (Single Correct Answer)

-0.25

The period of the function f(x) = cos 4x + tan 3x is

$$\pi$$

$${\pi \over 2}$$

$${\pi \over 3}$$

$${\pi \over 4}$$

WB JEE 2011

MCQ (Single Correct Answer)

-0.25

The even function of the following is

$$f(x) = {{{a^x} + {a^{ - x}}} \over {{a^x} - {a^{ - x}}}}$$

$$f(x) = {{{a^x} + 1} \over {{a^x} - 1}}$$

$$f(x) = x.\,{{{a^x} - 1} \over {{a^x} + 1}}$$

$$f(x) = {\log _2}(x + \sqrt {{x^2} + 1} )$$

WB JEE 2011

MCQ (Single Correct Answer)

-0.25

If f(x + 2y, x $$-$$ 2y) = xy, then f(x, y) is equal to

$${1 \over 4}xy$$

$${1 \over 4}({x^2} - {y^2})$$

$${1 \over 8}({x^2} - {y^2})$$

$${1 \over 2}({x^2} + {y^2})$$

WB JEE 2024

MCQ (Single Correct Answer)

-0.25

Let $$\mathrm{f}: \mathbb{R} \rightarrow \mathbb{R}$$ be a function defined by $$\mathrm{f}(x)=\frac{\mathrm{e}^{|x|}-\mathrm{e}^{-x}}{\mathrm{e}^x+\mathrm{e}^{-x}}$$, then

$$f$$ is both one-one and onto

$$f$$ is one-one but not onto

$$f$$ is onto but not one-one

$$f$$ is neither one-one nor onto

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