Let f(x) be a function such that , f(x-1...

Let f(x) be a function such that , `f(x-1)+f(c+1)=sqrt(3)f(x), forall x in R`. If f(5)=100, find `sum_(r=0)^(99)f(5+12r)`.

Text Solution

Verified by Experts

The correct Answer is:

2

Topper's Solved these Questions

FUNCTIONS
ARIHANT MATHS ENGLISH|Exercise Exercise (Subjective Type Questions)|13 Videos
FUNCTIONS
ARIHANT MATHS ENGLISH|Exercise FUNCTION EXERCISE 7: Subjective Type Questions|1 Videos
FUNCTIONS
ARIHANT MATHS ENGLISH|Exercise FUNCTION EXERCISE 5: Matching Type Questions|2 Videos
ESSENTIAL MATHEMATICAL TOOLS
ARIHANT MATHS ENGLISH|Exercise Exercise (Single Integer Answer Type Questions)|3 Videos
GRAPHICAL TRANSFORMATIONS
ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|10 Videos

Similar Questions

Explore conceptually related problems

Let f(x) be a function such that : f(x - 1) + f(x + 1) = sqrt3 f(x), for all x epsilon R. If f(5) = 100, then prove that the value of sum_(r=o)^99 f(5 + 12r) will be equal to 10000.

If f(x) is a function such that f(x-1)+f(x+1)=sqrt3t(x) and f(5)=100 , then find sum_(t=0)^(19)f(5+12r) .

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

Let f be a real vlaued fuction with domain R such that f(x+1)+f(x-1)=sqrt(2)f(x) for all x in R , then ,

Let f(x) be a continuous function such that f(0) = 1 and f(x)=f(x/7)=x/7 AA x in R, then f(42) is

Let f(x)=x+f(x-1) for AAx in R . If f(0)=1,f i n d \ f(100) .

Let f be a real valued function satisfying f(x+y)=f(x)+f(y) for all x, y in R and f(1)=2 . Then sum_(k=1)^(n)f(k)=

Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x for all x in (0,oo) and f(1)=1 , then

Let f:R->R be a function such that f((x+y)/3)=(f(x)+f(y))/3 ,f(0) = 0 and f'(0)=3 ,then

ARIHANT MATHS ENGLISH-FUNCTIONS-Exercise (Single Integer Answer Type Questions)

Let f(x) denotes the number of zeroes in f'(x). If f(m)-f(n)=3, the va...
Text Solution
|
If x^(2)+y^(2)=4 then find the maximum value of (x^(3)+y^(3))/(x+y)
Text Solution
|
Let f(n) denotes the square of the sum of the digits of natural numbe...
Text Solution
|
If [sinx]+[x/(2pi)]+[(2x)/(5pi)]=(9x)/(10pi), where [*] denotes the gr...
Text Solution
|
The number of integral solutions of 1/x+1/y=1/6 " with " x le y " is "...
Text Solution
|
If f(x) is a polynominal of degree 4 with leading coefficient '1' sati...
Text Solution
|
If a+b = 3- cos 4 theta and a-b =4 sin 2theta, then ab is always less ...
Text Solution
|
Let 'n' be the number of elements in the domain set of the function f(...
Text Solution
|
Let f(x) be a function such that , f(x-1)+f(c+1)=sqrt(3)f(x), forall x...
Text Solution
|
If 2f(x)=f(x y)+f(x/y) for all positive values of x and y,f(1)=0 and f...
Text Solution
|
Let f be a function from the set of positive integers to the set of re...
Text Solution
|
If f(x)=(x^(4)+x^(2)+1)/(x^(2)-x+1), the value of f(omega^(n)) (where ...
Text Solution
|
If f^2(x)*f((1-x)/(1+x))=x^3, [x!=-1,1 and f(x)!=0], then find |[f(-2)...
Text Solution
|
An odd function is symmetric about the vertical line x=a ,(a >0),a n d...
Text Solution
|
L e t(e^x-e^(-x))/(e^x+e^(-x))=lnsqrt((1+x)/(1-x)),then find x.
Text Solution
|
If x is real, the maximum value of (3x^(2)+9x+17)/(3x^(2)+9x+7) is (...
Text Solution
|
If f(x) satisfies the relation f(x)+f(x+4)=f(x+2)+f(x+6) for allx , th...
Text Solution
|
83. A non-zero function f (x) is symmetrical about the line y=x then t...
Text Solution
|
Let f:R rarr R and f(x)=(3x^(2)+mx+n)/(x^(2)+1). If the range of this ...
Text Solution
|
Let f(x)be a monotic ploynomial of degree (2m-1) where m in N Then the...
Text Solution
|