Home
Class 12
MATHS
Let f:R rarr R be a continuous function ...

Let `f:R rarr R` be a continuous function such that
`f(x)-2f(x/2)+f(x/4)=x^(2)`.
The equation f(x)-x-f(0)=0 have exactly

A

no solution

B

one solution

C

two solution

D

infinite solution

Text Solution

Verified by Experts

The correct Answer is:
c
Promotional Banner

Similar Questions

Explore conceptually related problems

Let f:R rarr R be a continuous function such that f(x)-2f(x/2)+f(x/4)=x^(2) . f(3) is equal to

Let f:R rarr R be a continuous function such that f(x)-2f(x/2)+f(x/4)=x^(2) . f'(0) is equal to

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

Let f : (0, oo) rarr R be a continuous function such that f(x) = int_(0)^(x) t f(t) dt . If f(x^(2)) = x^(4) + x^(5) , then sum_(r = 1)^(12) f(r^(2)) , is equal to

If the system of equations 2x-y+z=0,x-2y+z=0, tx-y+2z=0 has infinitely many solution and f(x) be a continuous function such that f(5+x)+f(x)=2 , then int_(0)^(-2t) f(x) dx is equal to

If f(x)> x ;AA x in R. Then the equation f(f(x))-x=0, has

Prove that f(x)= 2x-|x| is a continuous function at x= 0.

If f:R rarr R is continuous function satisfying f(0) =1 and f(2x) -f(x) =x, AAx in R , then lim_(nrarroo) (f(x)-f((x)/(2^(n)))) is equal to

Let f is a differentiable function such that f'(x) = f(x) + int_(0)^(2) f(x) dx, f(0) = (4-e^(2))/(3) , find f(x).

Let f : R rarr R be the function defined by f(x) = 2x - 2 , AA x in R . Write f^(-1) .