Home
Class 12
MATHS
{ . } denotes the fractional part functi...

{ . } denotes the fractional part function and [.] denotes the greatest integer function. Now, match the following lists:

Text Solution

Verified by Experts

The correct Answer is:
`a to s; b to r; c to s; d to p`
a. `f(x)=e^(cos^(4)pix+x-[x]+cos^(2)px)`
`cos^(2)pi x " and " cos^(4)pi x` have period 1.
`x-[x]={x}` has period 1.
Then the period of `f(x)` is 1
b. `f(x)=cos 2pi {2x}+sin 2pi{2x}`
The period of {2x} is 1/2. Then the period of `f(x)` is 1/2.
c. Clearly, `tan pi[x]=0 AA x in R` and the period of `sin 3pi{x}` is equal 1.
d. `f(x)=3x-[3x+a]-b=3x+a-[3x+a]-(a+b)`
`={3x+a}-(a+b)`
Thus, the period of `f(x)` is 1/3.
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE ENGLISH|Exercise Numerical value Type|31 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE ENGLISH|Exercise Archives(single correct Answer Type)|9 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE ENGLISH|Exercise Linked Comprehension Type|32 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE ENGLISH|Exercise Archives (Numerical Value Type)|3 Videos

  • SCALER TRIPLE PRODUCTS

    CENGAGE ENGLISH|Exercise DPP 2.3|11 Videos

Similar Questions

Explore conceptually related problems

If F(x)=(sinpi[x])/({x}) then F(x) is (where {.} denotes fractional part function and [.] denotes greatest integer function and sgn(x) is a signum function)

In the following ,[x] denotes the greatest integer less than or equal to x. Now, match th following lists:

If f(x)=[sin^(2) x] ([.] denotes the greatest integer function), then

Draw the graph of y=[|x|] , where [.] denotes the greatest integer function.

If f(x) =[|x|] where [.] denotes the greatest integer function , then which of the following is not true ?

If [.] denotes the greatest integer function, then f(x)=[x]+[x+(1)/(2)]

Lt_(xto2) [x] where [*] denotes the greatest integer function is equal to

the value of int_(0)^([x]) dx (where , [.] denotes the greatest integer function)

The function f(x)={x} , where [x] denotes the greatest integer function , is continuous at

The function, f(x)=[|x|]-|[x]| where [] denotes greatest integer function: