JEE Main 2022 (Online) 25th June Morning Shift | Functions Question 68 | Mathematics

Let $$f:R \to R$$ and $$g:R \to R$$ be two functions defined by $$f(x) = {\log _e}({x^2} + 1) - {e^{ - x}} + 1$$ and $$g(x) = {{1 - 2{e^{2x}}} \over {{e^x}}}$$. Then, for which of the following range of $$\alpha$$, the inequality $$f\left( {g\left( {{{{{(\alpha - 1)}^2}} \over 3}} \right)} \right) > f\left( {g\left( {\alpha -{5 \over 3}} \right)} \right)$$ holds ?

(2, 3)

($$-$$2, $$-$$1)

(1, 2)

($$-$$1, 1)

JEE Main 2021 (Online) 1st September Evening Shift

MCQ (Single Correct Answer)

-1

The range of the function,

$$f(x) = {\log _{\sqrt 5 }}\left( {3 + \cos \left( {{{3\pi } \over 4} + x} \right) + \cos \left( {{\pi \over 4} + x} \right) + \cos \left( {{\pi \over 4} - x} \right) - \cos \left( {{{3\pi } \over 4} - x} \right)} \right)$$ is :

$$\left( {0,\sqrt 5 } \right)$$

[$$-$$2, 2]

$$\left[ {{1 \over {\sqrt 5 }},\sqrt 5 } \right]$$

[0, 2]

JEE Main 2021 (Online) 31st August Evening Shift

MCQ (Single Correct Answer)

-1

Let f : N $$\to$$ N be a function such that f(m + n) = f(m) + f(n) for every m, n$$\in$$N. If f(6) = 18, then f(2) . f(3) is equal to :

JEE Main 2021 (Online) 27th July Evening Shift

MCQ (Single Correct Answer)

-1

Let f : R $$\to$$ R be defined as $$f(x + y) + f(x - y) = 2f(x)f(y),f\left( {{1 \over 2}} \right) = - 1$$. Then, the value of $$\sum\limits_{k = 1}^{20} {{1 \over {\sin (k)\sin (k + f(k))}}} $$ is equal to :

cosec²(21) cos(20) cos(2)

sec²(1) sec(21) cos(20)

cosec²(1) cosec(21) sin(20)

sec²(21) sin(20) sin(2)

PREVIOUS NEXT

Questions Asked from Functions (MCQ (Single Correct Answer))

Number in Brackets after Paper Indicates No. of Questions