The function f ( x ) = sec log x + 1 + x 2 is

neither an odd nor an even function

The function f x = log x + x 2 + 1 is

Neither an even nor an odd function

HARD

Earn 100

Let $f$ be an odd function defined on the real number such that $f (x) = 3 \sin x + 4 \cos x$ $,$ for $x \geq 0$ $,$ then $f (x)$ for $x < 0$ is

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Important Questions on Functions

EASY

Mathematics>Differential Calculus>Functions>Even and Odd Functions

Let

f (- x) = f (x)

. Then

f^{'} (x)

must be

EASY

Mathematics>Differential Calculus>Functions>Even and Odd Functions

Which of the following functions is neither even nor odd?

EASY

Mathematics>Differential Calculus>Functions>Even and Odd Functions

The even function of the following is

MEDIUM

Mathematics>Differential Calculus>Functions>Even and Odd Functions

The function

f (x) = \sec [\log (x + \sqrt{1 + x^{2}})]

MEDIUM

Mathematics>Differential Calculus>Functions>Even and Odd Functions

Let

[t]

denote the greatest integer

\leq t

and

\lim_{x \to 0} x [\frac{4}{x}] = A .

Then the function,

f (x) = [x^{2}] \sin (π x)

is discontinuous, when

x

is equal to:

MEDIUM

Mathematics>Differential Calculus>Functions>Even and Odd Functions

The function

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

MEDIUM

Mathematics>Differential Calculus>Functions>Even and Odd Functions

The real valued function

f (x) = \frac{x}{e^{x} - 1} + \frac{x}{2} + 1

defined on

R \ {0}

EASY

Mathematics>Differential Calculus>Functions>Even and Odd Functions

f : R \to R,

such that

f (x) = \frac{e^{x} + e^{- x}}{e^{x} - e^{- x}},

then

f

HARD

Mathematics>Differential Calculus>Functions>Even and Odd Functions

Let

f (x) = a^{x} (a > 0)

be written as

f (x) = f_{1} (x) + f_{2} (x),

where

f_{1} (x)

is an even function and

f_{2} (x)

is an odd function. Then

f_{1} (x + y) + f_{1} (x - y)

equals:

HARD

Mathematics>Differential Calculus>Functions>Even and Odd Functions

a \in R

and the equation

- 3 (x - [x])^{2} + 2 (x - [x]) + a^{2} = 0

(where

[x]

denotes the greatest integer

\leq

x

) has no integral solution, then all possible values of

a

lie in the interval

HARD

Mathematics>Differential Calculus>Functions>Even and Odd Functions

Let

f : R \to R

be such that

f (1) = 3

and

f' (1) = 6

, Then,

\lim_{x \to 0} {\{\frac{f (1 + x)}{f (1)}\}}^{1 / x}

is equal to

HARD

Mathematics>Differential Calculus>Functions>Even and Odd Functions

\lim_{x \to {\frac{π}{2}}^{-}} {[1 + {(\cos x)}^{\cos x}]}^{2}

is equal to

HARD

Mathematics>Differential Calculus>Functions>Even and Odd Functions

The function

f : C \to C

defined by

f (x) = \frac{a x + b}{c x + d}

for

x \in C

where

b d \neq 0

reduces to a constant function, if

EASY

Mathematics>Differential Calculus>Functions>Even and Odd Functions

The function

f (x)

which satisfies

f (x) = f (- x) = \frac{f^{'} (x)}{x}

, is given by

HARD

Mathematics>Differential Calculus>Functions>Even and Odd Functions

The function f (x) is an even function and satisfies

x^{2} f (x) - 2 f (\frac{1}{x}) = g (x)

where g(x) is an odd function, then f (5) equals

MEDIUM

Mathematics>Differential Calculus>Functions>Even and Odd Functions

f : R \to R;

f (x) = (\frac{e^{2 x} - 1}{e^{2 x} + 1})

HARD

Mathematics>Differential Calculus>Functions>Even and Odd Functions

\lim_{n \to \infty} \prod_{r = 3}^{n} \frac{r^{3} - 8}{r^{3} + 8}

equals to

MEDIUM

Mathematics>Differential Calculus>Functions>Even and Odd Functions

[si n^{- 1} x] > [co s^{- 1} x]

where [.] denotes greatest integer function, then the range of ‘

x

’ contains (also

x > 0

)

EASY

Mathematics>Differential Calculus>Functions>Even and Odd Functions

f (x) = 4 x^{8}

, then

HARD

Mathematics>Differential Calculus>Functions>Even and Odd Functions

f (x) = 4 x^{3} - x^{2} - 2 x + 1

and

g (x) = \{\begin{matrix} \min \{f (t) : 0 \leq t \leq x\}; & 0 \leq x \leq 1 \\ 3 - x; & 1 < x \leq 2 \end{matrix}

then

g (\frac{1}{4}) + g (\frac{3}{4}) + g (\frac{5}{4})

has the value equal to

Let f be an odd function defined on the real number such that fx=3sin⁡x+4cos⁡x , for x≥0 , then f(x) for x<0 is

Important Questions on Functions

Learn and Prepare for any exam you want !

Let $f$ be an odd function defined on the real number such that $f (x) = 3 \sin x + 4 \cos x$ $,$ for $x \geq 0$ $,$ then $f (x)$ for $x < 0$ is