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`

Answer

Step by step text solution for Let f(x+y)=f(x)f(y) for all x,y in Rand f(0)!=0. Let phi(x)=f(x)/(1+f(x)^2). Then prove that phi(x)-phi(-x)=0 by MATHS experts to help you in doubts & scoring excellent marks in Class 12 exams.

Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    AAKASH INSTITUTE|Exercise Assignment (Section - I) Subjective Type Questions|15 Videos
  • PROBABILITY

    AAKASH INSTITUTE|Exercise ASSIGNMENT SECTION-J (aakash challengers questions)|13 Videos
  • SEQUENCES AND SERIES

    AAKASH INSTITUTE|Exercise Assignment (SECTION - J) Aakash Challengers|12 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

Let f(x+2y)=f(x)(f(y))^(2) for all x,y and f(0)=1. If f is derivable at x=0 then f'(x)=

Knowledge Check

  • 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

    A
    One-one function
    B
    Onto function
    C
    Even function
    D
    Odd function
  • Let f(x+y)=f(x).f(y) for all x, y in R and f(x)=1+x phi(x)log3. If lim_(xrarr0)phi(x)=1, then f'(x) is equal to

    A
    `log3^(f(x))`
    B
    `log[f(x)]^(3)`
    C
    `log3`
    D
    None of these
  • Let f(x+y)=f(x)f(y) for all x and y. If f(5)=2 and f'(0)=3 then f'(5) is equal to

    A
    5
    B
    8
    C
    0
    D
    none of these
  • Similar Questions

    Explore conceptually related problems

    Let phi(a)=f(x)+f(2ax) and f'(x)>0 for all x in[0,a]. Then ,phi(x)

    Let f(x+y)=f(x)+f(y) for all real x,y and f'(0) exists.Prove that f'(x)=f'(0) for all x in R and 2f(x)=xf(2)

    Let f(x+y)=f(x)f(y) for all x,y in R suppose that f(3)=3,f(0)!=0 and f'(0)=11, then f'(3) is equal

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

    Let f(x+y)=f(x)*f(y) for all x y where f(0)!=0 .If f(5)=2 and f'(0)=3 then f'(5) is equal to