Let ' f ' be an even periodic function with period ' 4 ' such that f x = 2 x - 1 , 0 ≤ x ≤ 2 . The number of solutions of the equation f x = 1 in - 10 , 20 are

Given, f x = 2 x - 1 and also given f x is even, so f - x = f x and f x + 4 = f x as time period is 4 , Now plotting the graph of the function for the above data we have, Now plotting the diagram of f x = 1 we get, Now from diagram we can see there is one intersecting point in - 6 , 0 , - 4 , 0 , - 2 , 0 , 0 , 2 , 2 , 0 , 6 , 0 . . . . . . . . . So there will be total 15 intersection point between - 10 , 20 .

Let ' f ' be an even periodic function with period ' 4 ' such that f x = 2 x - 1 , 0 ≤ x ≤ 2 . The number of solutions of the equation f x = 1 in - 10 , 20 are

Given, f x = 2 x - 1 and also given f x is even, so f - x = f x and f x + 4 = f x as time period is 4 , Now plotting the graph of the function for the above data we have, Now plotting the diagram of f x = 1 we get, Now from diagram we can see there is one intersecting point in - 6 , 0 , - 4 , 0 , - 2 , 0 , 0 , 2 , 2 , 0 , 6 , 0 . . . . . . . . . So there will be total 15 intersection point between - 10 , 20 .

The function f x = sin π x n ! − cos π x n + 1 ! is

periodic, with period 2 n + 1 !

Which of the following functions are periodic? (Where · denotes the greatest integer function.)

p x = x + x + 1 3 + x + 2 3 - 3 x + 1 0 , where [.] denotes the greatest integer function.

MEDIUM

Earn 100

Let $' f'$ be an even periodic function with period $' 4'$ such that $f (x) = 2^{x} - 1, 0 \leq x \leq 2$ . The number of solutions of the equation $f (x) = 1$ in $[- 10, 20]$ are

Important Questions on Functions

MEDIUM

Mathematics>Differential Calculus>Functions>Periodic Functions

The function

f (x) = \sin (\frac{π x}{n!}) - \cos (\frac{π x}{(n + 1)!})

EASY

Mathematics>Differential Calculus>Functions>Periodic Functions

The period of the function

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

MEDIUM

Mathematics>Differential Calculus>Functions>Periodic Functions

The period of

\sin^{2} θ

EASY

Mathematics>Differential Calculus>Functions>Periodic Functions

Consider the function

f (x) = \cos x^{2}

. Then

HARD

Mathematics>Differential Calculus>Functions>Periodic Functions

a, b

be two fixed positive integers such that

f (a + x) = b + {[b^{3} + 1 - 3 b^{2} f (x) + 3 b {\{f (x)\}}^{2} - {\{f (x)\}}^{3}]}^{1 / 3}

for all real

x

then

f (x)

is a periodic function with period

EASY

Mathematics>Differential Calculus>Functions>Periodic Functions

The function

f (x) = \tan π x - x + [x]

has period, where

[.]

denotes greatest integer function

EASY

Mathematics>Differential Calculus>Functions>Periodic Functions

f (a + x) = f (x)

, then

\int_{0}^{n a} f (x) d x

, where

n \in N

, is equal to

EASY

Mathematics>Differential Calculus>Functions>Periodic Functions

f : R \to R

is a function satisfying

f (2 x + 3) + f (2 x + 7) = 2 \forall x \in R

, then the period of

f (x)

EASY

Mathematics>Differential Calculus>Functions>Periodic Functions

Let $f (x) = \sin x + \cos a x$ be a periodic function. Then,

MEDIUM

Mathematics>Differential Calculus>Functions>Periodic Functions

The function $f (x) = |sin 4 x| + |cos 2 x|,$ is a periodic function with a fundamental period

EASY

Mathematics>Differential Calculus>Functions>Periodic Functions

The period of

\sin^{4} x + \cos^{4} x

HARD

Mathematics>Differential Calculus>Functions>Periodic Functions

f (x) = 2^{s i n^{3} π x + x - [x]}

, where

[\cdot]

denotes the integral part of

x

is a periodic function with period

EASY

Mathematics>Differential Calculus>Functions>Periodic Functions

The period of

\sin^{2} θ

MEDIUM

Mathematics>Differential Calculus>Functions>Periodic Functions

The period of the function

f (θ) = 4 + 4 \sin^{3} θ - 3 \sin θ

HARD

Mathematics>Differential Calculus>Functions>Periodic Functions

Which of the following functions are periodic? (Where

[\cdot]

denotes the greatest integer function.)

MEDIUM

Mathematics>Differential Calculus>Functions>Periodic Functions

The period of the function

f (θ) = \sin \frac{θ}{3} + \cos \frac{θ}{2}

HARD

Mathematics>Differential Calculus>Functions>Periodic Functions

The period of the function

f (x) = [\sin 3 x] + |\cos 6 x|

is (

[.]

denotes the greatest integer less than or equal to

x

)

MEDIUM

Mathematics>Differential Calculus>Functions>Periodic Functions

\sin a x + \cos a x

and

|\sin x| + |\cos x|

are periodic with the same fundamental period, if

a

equals to

HARD

Mathematics>Differential Calculus>Functions>Periodic Functions

If f be a real value function such that for any real $x, f (15 + x) = f (15 - x) & f (30 + x) = - f (30 - x)$ , then which of the following statement is true ?

EASY

Mathematics>Differential Calculus>Functions>Periodic Functions

The fundamental period of the function

f (x) = |\sin x| + |\cos x|

Let 'f' be an even periodic function with period '4' such that fx=2x-1, 0≤x≤2. The number of solutions of the equation fx=1 in -10,20 are

Important Questions on Functions

Learn and Prepare for any exam you want !

Let $' f'$ be an even periodic function with period $' 4'$ such that $f (x) = 2^{x} - 1, 0 \leq x \leq 2$ . The number of solutions of the equation $f (x) = 1$ in $[- 10, 20]$ are