Home
Class 11
MATHS
Let f:R rarr R be a continuous function ...

Let `f:R rarr R` be a continuous function such that `f(x)-2 f(x/2) + f(x/4)=x^(2)`. Now answer the following
`f(3)=`

A

no solution

B

one solution

C

two solution

D

infinite solutions

Text Solution

Verified by Experts

The correct Answer is:
C
Doubtnut Promotions Banner Mobile Dark
|

Similar Questions

Explore conceptually related problems

Let R rarr R be a continuous function define by f(x ) = (1)/(e^(x)+2e) statement 1 : f(c )=1/3 for some c in R statement 2 0 lt f(x) le (1)/(2sqrt(2)) for all x in R

f: R^(+) rarr R is continuous function satisfying f(x/y)=f(x) - f (y) AA x, y in R^(+) . If f'(1) = 1, then

Knowledge Check

  • Let f:R rarr R be a continuous function such that f(x)-2 f(x/2) + f(x/4)=x^(2) . Now answer the following f(0)=

    A
    0
    B
    1
    C
    `f(0)`
    D
    `-f(0)`
  • Let f:R to R be a continuous function and f(x)=f(2x) is true AA x in R . If f(1) = 3 then the value of int_(-1)^(1) f(f(x))dx=

    A
    6 or 2f(0)
    B
    0
    C
    3f(x)
    D
    3f(0)
  • let f: R to R be a function such that f(2-x)= f(2+x) and f(4-x)=f(4+x) , for all x in R and int_(0)^(2)f(x)dx=5 . Then the value of int_(10)^(50) f(x) dx is

    A
    125
    B
    80
    C
    100
    D
    200
  • Similar Questions

    Explore conceptually related problems

    Let f:R to R be a function such that |f(x)|le x^(2),"for all" x in R. then at x=0, f is

    Let f(x) = (1)/(2) [f( xy ) + f((x)/(y)) ]AA x, y in R ^(+) such that f(1) = 0, f^(1) (1)=2 Now answer the following f(x) - f(y ) =

    Let f : R rarr R be a differentiable function satisfying f(x+y)=f(x) + f(y) +x^2y+xy^2 for all real number x and y . If lim_(x rarr 0)(f(x))/x = 1 , then The value of f'(3) is

    Let f: R rarr R be a function defined by f(x)=(x^(2)+2x+5)/(x^(2)+x+1) is

    Let f(x) = (1)/(2) [f( xy ) + f((x)/(y)) ]AA x, y in R ^(+) such that f(1) = 0, f^(1)(1) =2 Now answer the following f(e) =