Home
Class 12
MATHS
Let f: R->R satisfying f((x+y)/k)=(f(...

Let `f: R->R` satisfying `f((x+y)/k)=(f(x)+f(y))/k( k != 0,2)`.Let `f(x)` be differentiable on `R and f'(0) = a`, then determine `f(x)`.

A

even function

B

neither even nor odd function

C

either zero or odd function

D

either zero or even function

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Similar Questions

Explore conceptually related problems

Let f : R rarr R satisfying |f(x)|le x^(2), AA x in R , then show that f(x) is differentiable at x = 0.

Let f:R->R be a function such that f(x+y)=f(x)+f(y),AA x, y in R.

A function f : R to R satisfies the equation f(x+y) = f (x) f(y), AA x, y in R and f (x) ne 0 for any x in R . Let the function be differentiable at x = 0 and f'(0) = 2. Show that f'(x) = 2 f(x), AA x in R. Hence, determine f(x)

Let f(x) be a differentiable function in the interval (0, 2) then the value of int_(0)^(2)f(x)dx

A function f : R rarr R satisfies the equation f(x + y) = f(x) . f(y) for all, f(x) ne 0 . Suppose that the function is differentiable at x = 0 and f'(0) = 2. Then,

A function f: R rarr R satisfies the equation f(x+ y)= f(x).f(y) "for all" x, y in R, f(x) ne 0 . Suppose that the function is differentiable at x=0 and f'(0)=2, then prove that f'(x)= 2f(x)

If f(x)= int_(0)^(x)(f(t))^(2) dt, f:R rarr R be differentiable function and f(g(x)) is differentiable at x=a , then

Let f((x+y)/2)=(f(x)+f(y))/2 for all real x and y. If f'(0) exists and equals -1 and f(0)=1, find f(2)

f:R->R is defined as f(x)=2x+|x| then f(3x)-f(-x)-4x=

Let f:R->R be a function satisfying f((x y)/2)=(f(x)*f(y))/2,AAx , y in R and f(1)=f'(1)=!=0. Then, f(x)+f(1-x) is (for all non-zero real values of x ) a.) constant b.) can't be discussed c.) x d.) 1/x