Home
Class 12
MATHS
Let f(x+y)=f(x)f(y) for all x,y in Rand ...

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`

Text Solution

AI Generated Solution

Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (Section - I) Subjective Type Questions|17 Videos

  • PROBABILITY

    AAKASH INSTITUTE ENGLISH|Exercise ASSIGNMENT SECTION-J (aakash challengers questions)|11 Videos

  • SEQUENCES AND SERIES

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (SECTION - J) Aakash Challengers|11 Videos

Similar Questions

Explore conceptually related problems

Let f(x+y)+f(x-y)=2f(x)f(y) AA x,y in R and f(0)=k , then

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:

Let f(x+y) + f(x-y) = 2f(x)f(y) for x, y in R and f(0) != 0 . Then f(x) must be

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)dotf(y) for all real x , ya n df(0)!=0, then prove that the function g(x)=(f(x))/(1+{f(x)}^2) is an even function.

If f(x+y)=f(x)dotf(y) for all real x , ya n df(0)!=0, then prove that the function g(x)=(f(x))/(1+{f(x)}^2) is an even function.

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

Let f:R to R such that f(x+y)+f(x-y)=2f(x)f(y) for all x,y in R . Then,

Let f(x)=1/2[f(xy)+f(x/y)] " for " x,y in R^(+) such that f(1)=0,f'(1)=2. f(x)-f(y) is equal to

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

Home
Profile