Home
Class 12
MATHS
If f (x+y) =f (x) f(y) for all x,y and ...

If `f (x+y) =f (x) f(y)` for all x,y and `f (0) ne 0, and F (x) =(f(x))/(1+(f (x))^(2))` then:

A

even function

B

odd function

C

odd if f(x)>0

D

neither even nor odd

Text Solution

Verified by Experts

The correct Answer is:
B, D
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE AND DEFINITE INTEGRATION

    VK JAISWAL ENGLISH|Exercise EXERCISE (COMPREHENSION TYPE PROBLEMS)|16 Videos
  • INDEFINITE AND DEFINITE INTEGRATION

    VK JAISWAL ENGLISH|Exercise EXERCISE (MATCHING TYPE PROBLEMS)|2 Videos
  • INDEFINITE AND DEFINITE INTEGRATION

    VK JAISWAL ENGLISH|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|29 Videos
  • HYPERBOLA

    VK JAISWAL ENGLISH|Exercise Exercise-4 : Subjective Type Problems|3 Videos
  • INVERSE TRIGONOMETRIC FUNTIONS

    VK JAISWAL ENGLISH|Exercise Exercise-5 : Subjective Type Problems|6 Videos

Similar Questions

Explore conceptually related problems

If f((x+y)/3)=(2+f(x)+f(y))/3 for all x,y f'(2)=2 then find f(x)

Let f(x+y)=f(x)f(y) for all x,y in R and f(0)!=0 . Let phi(x)=f(x)/(1+f(x)^2) . Then prove that phi(x)-phi(-x)=0

If f(x+y)=f(x) xx f(y) for all x,y in R and f(5)=2, f'(0)=3, then f'(5)=

If f (x/y)= f(x)/f(y) , AA y, f (y)!=0 and f' (1) = 2 , find f(x) .

If f (x/y)= f(x)/f(y) , AA y, f (y)!=0 and f' (1) = 2 , find f(x) .

Let a real valued function f satisfy f(x + y) = f(x)f(y)AA x, y in R and f(0)!=0 Then g(x)=f(x)/(1+[f(x)]^2) is

If f(x-y), f(x) f(y), and f(x+y) are in A.P. for all x, y, and f(0) ne 0, then

If f(x-y), f(x) f(y), and f(x+y) are in A.P. for all x, y, and f(0) ne 0, then

If f((x)/(y))=(f(x))/(f(y)) forall x, y in R, y ne 0 and f'(x) exists for all x, f(2) = 4 . Then, f(5) is

If f(x+y)=2f(x) f(y) for all x,y where f'(0)=3 and f(4)=2, then f'(4) is equal to