A real valued function f(x) satisfies th...

A real valued function f(x) satisfies the functional equation `f(x-y) = f(x) f(y) - f(a-x) f(a+y)`, where a is a given constant and f(0)=1 , f(2a-x) =?

`-f(x)`

`f(x)`

`f(a)+ f(a-x)`

`f(-x)`

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

FUNCTION
VK JAISWAL ENGLISH|Exercise ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT|23 Videos
FUNCTION
VK JAISWAL ENGLISH|Exercise COMPREHENSION TYPE PROBLEMS|15 Videos
ELLIPSE
VK JAISWAL ENGLISH|Exercise Exercise-4 : Subjective Type Problems|2 Videos
HYPERBOLA
VK JAISWAL ENGLISH|Exercise Exercise-4 : Subjective Type Problems|3 Videos

Similar Questions

Explore conceptually related problems

A real-valued functin f(x) satisfies the functional equation f(x-y)=f(x)f(y)-f(a-x)f(a+y), where a given constant and f(0)=1. Then prove that f(x) is symmetrical about point (a, 0).

If a real valued function f(x) satisfies the equation f(x +y)=f(x)+f (y) for all x,y in R then f(x) is

The function f(x) satisfying the equation f^2 (x) + 4 f'(x) f(x) + (f'(x))^2 = 0

A function f(x) satisfies the relation f(x+y) = f(x) + f(y) + xy(x+y), AA x, y in R . If f'(0) = - 1, then

A function f : R→R satisfies the equation f(x)f(y) - f(xy) = x + y ∀ x, y ∈ R and f (1)>0 , then

If the function / satisfies the relation f(x+y)+f(x-y)=2f(x),f(y)AAx , y in R and f(0)!=0 , then

A function f (x) is defined for all x in R and satisfies, f(x + y) = f (x) + 2y^2 + kxy AA x, y in R , where k is a given constant. If f(1) = 2 and f(2) = 8 , find f(x) and show that f (x+y).f(1/(x+y))=k,x+y != 0 .

Let f(x) be a real valued function satisfying the relation f(x/y) = f(x) - f(y) and lim_(x rarr 0) f(1+x)/x = 3. The area bounded by the curve y = f(x), y-axis and the line y = 3 is equal to

Let f(x) be a function satisfying f(x+y)=f(x)+f(y) and f(x)=x g(x)"For all "x,y in R , where g(x) is continuous. Then,

A function f: R -> R satisfy the equation f (x)f(y) - f (xy)= x+y for all x, y in R and f(y) > 0 , then

VK JAISWAL ENGLISH-FUNCTION -SUBJECTIVE TYPE PROBLEMS

A real valued function f(x) satisfies the functional equation f(x-y) ...
Text Solution
|
Let f(x) be a polynomial of degree 6 with leading coefficient 2009. Su...
Text Solution
|
Let f (x) =x ^(3)-3x Find f (f (x))
Text Solution
|
If f(x+y+1)={sqrt(f(x))+sqrt(f(y))}^2 and f(0)=1AAx ,y in R ,d e t e ...
Text Solution
|
If the domain of f(x) = sqrt (12-3^(x)-3^(3-x))+ sin ^(-1) ((2x)/(3 ...
Text Solution
|
The number of elements in the range of functions: y=sin^(-1) [x^(2)+5/...
Text Solution
|
The number of integers in the range of function f (x) = [ sin x] + [ s...
Text Solution
|
If P (x) is polynomial of degree 4 such than P (-1)=P (1) =5 and P (-2...
Text Solution
|
The number of integral vlaue (s) of k for which the curve y = sqrt ( ...
Text Solution
|
Let the solution set of the equation : sqrt([x+[(x)/(2)]])+ sqrt((x)...
Text Solution
|
For the real number x, let f (x)=(1)/( ""^(2011sqrt(1-x^(2011)))). Fi...
Text Solution
|
Find the number of elements contained in the range of the function f (...
Text Solution
|
Let f (x,y)= x^(2) - y^(2) and g (x,y) = 2xy. such that (f ( x,y))^(2)...
Text Solution
|
Let f (x) = (x+5)/(sqrt(x^(2)) +1) AA x in R, then the smallest integr...
Text Solution
|
The number of integral values of a for which f (x) = x^(3) +(a+2) x ^(...
Text Solution
|
The number of roots of equation (((x-1)(x-3))/((x-2)(x-4))-e^(x)) (((x...
Text Solution
|
The number of solutions of the equation cos ^(-1)((1-x ^(2) -2x)/((x+...
Text Solution
|
Let f(x)=x^2-bx+c,b is an odd positive integer. Given that f(x)=0 ha...
Text Solution
|
Let f(x) be a continuous function such that f(0) = 1 and f(x)=f(x/7)=x...
Text Solution
|
If f (x) = 4x ^(3) -x ^(2) -2x +1 and g (x) = {{:(min {f(t): 0 le t le...
Text Solution
|
If x=10 sum(r=3) ^(100) (1)/((r ^(2) -4)), then [x]= (where [.] deno...
Text Solution
|