Home
Class 12
MATHS
Identify the following functions whether...

Identify the following functions whether odd or even or neither: `f(x)=cos["x"]+[(sinx)/2]` where `[dot]` denotes the greatest integer function.

A

Odd

B

Even

C

Neither

D

Both

Text Solution

Verified by Experts

The correct Answer is:
C
`0 le |(sinx)/(2)| le (1)/(2) " or " [|(sinx)/(2)|]=0`
Therefore, `f(x)=cosx,` which is even.
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise 1.11|7 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise 1.12|9 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise 1.9|13 Videos

  • Quadratic Equations, Inequalities, Modulus and Logarithms

    CENGAGE|Exercise Question Bank|28 Videos

  • SCALER TRIPLE PRODUCTS

    CENGAGE|Exercise DPP 2.3|11 Videos

Similar Questions

Explore conceptually related problems

Identify the following functions whether odd or even or neither: f(x)=cos|x|+[|(sinx)/2|] where [dot] denotes the greatest integer function.

Identify the following functions whether odd or even or neither: f(x)={ x|x| for x =1

Identify the following functions whether odd or even or neither: f(x)=xg(x)g(-x)+"tan"(sinx)

Identify the following functions whether odd or even or neither: f(x) = {g(x) - g( - x)}

Identify the following functions whether odd or even or neither: f(x)=log((x^4+x^2+1)/(x^2+x+1))

Solve x^2-4-[x]=0 (where [] denotes the greatest integer function).

Draw the graph of y = cos x, x in [0, 2pi], where [*] denotes the greatest integer function.

Evaluate: int_(-5)^5x^2[x+1/2]dx(w h e r e[dot] denotes the greatest integer function).

Draw the graph of f(x) = [x^(2)], x in [0, 2) , where [*] denotes the greatest integer function.