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

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

Neither an even nor an odd function

EASY

Earn 100

The below function is even, odd, or neither even nor odd?

$y = x \cdot \frac{a^{x} - 1}{a^{x} + 1}$

Important Questions on Functions

MEDIUM

Mathematics>Differential Calculus>Functions>Even and Odd Functions

The function

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

EASY

Mathematics>Differential Calculus>Functions>Even and Odd Functions

Let

f (- x) = f (x)

. Then

f^{'} (x)

must be

HARD

Mathematics>Differential Calculus>Functions>Even and Odd Functions

P (x)

be a polynomial with real coefficients such that

P ({s i n}^{2} x) = P ({c o s}^{2} x),

for all

x \in [0, \frac{π}{2}] .

Consider the following statements:

I.

P (x)

is an even function.

II.

P (x)

can be expressed as a polynomial in

{(2 x - 1)}^{2}

III.

P (x)

is a polynomial of even degree. Then

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

Which of the following functions is neither even nor odd?

MEDIUM

Mathematics>Differential Calculus>Functions>Even and Odd Functions

The function

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

EASY

Mathematics>Differential Calculus>Functions>Even and Odd Functions

The even function of the following is

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:

MEDIUM

Mathematics>Differential Calculus>Functions>Even and Odd Functions

f (x)

is an odd periodic function with period 2, then

f (4)

equals

HARD

Mathematics>Differential Calculus>Functions>Even and Odd Functions

Let $f (x) = \frac{s i n^{101} x}{[\frac{x}{π}] + \frac{1}{2}}$ , where $[x]$ denotes the integral part of $x$ is

MEDIUM

Mathematics>Differential Calculus>Functions>Even and Odd Functions

f : R \to R

is an even function having derivatives of all orders, then an odd function among the following is

EASY

Mathematics>Differential Calculus>Functions>Even and Odd Functions

The function

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

HARD

Mathematics>Differential Calculus>Functions>Even and Odd Functions

Let

f (x) = \frac{s i n^{101} x}{[\frac{x}{π}] + \frac{1}{2}}

, where

[x]

denotes the integral part of

x,

then

f (x)

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

Let f be an odd function defined on the set of real numbers such that for

x ⩾ 0

f (x) = 3 \sin x + 4 \cos x

, then

f (x)

x = - \frac{11 π}{6}

is equal to

EASY

Mathematics>Differential Calculus>Functions>Even and Odd Functions

f (x) = 4 x^{8}

, then

EASY

Mathematics>Differential Calculus>Functions>Even and Odd Functions

The graph of the function $y = f (x)$ is symmetrical about the line $x = 2$ , then

EASY

Mathematics>Differential Calculus>Functions>Even and Odd Functions

f (x) = 2017 \tan |x| + 3 x^{3} \sin x + x^{2018} - 3 x^{2} + 2 x^{3}

and

f (3) = 116,

then

f (- 3)

is equal to

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

The below function is even, odd, or neither even nor odd? y=x·ax-1ax+1

Important Questions on Functions

Learn and Prepare for any exam you want !

The below function is even, odd, or neither even nor odd?

$y = x \cdot \frac{a^{x} - 1}{a^{x} + 1}$