If f(x) satisfies the equation |[f(x+1),f(x+8),f(x+1)],[1,2,-5],[2,3,lambda]|=0 for all real x .If f is periodic with period 7 ,then the value of | lambda |

If f(x) satisfies he equation |(f(x + 1), f(x+8), f(x + 1)), (1,2,-5), (2,3,lambda)| = 0 for all real x. If f is periodic with period 7, then find the value of |lambda|.

If f(x) satisfies the equation |[f(x-3),f(x+4),f((x+1)(x-2)-(x-1)^(2))],[5,4,-5],[5,6,15]|=0 for all real x then (A) f(x) is not periodic (B) f(x) is periodic and is of period 1 (C) f(x) is periodic and is of period 7 (D) f(x) is an odd function

Consider function f satisfying f(x+4)+f(x-4)=f(x) for all real x .Then f(x) is periodic with period

If f(x) satisfies the relation f(x)+f(x+4)=f(x+2)+f(x+6) for all x, then prove that f(x) is periodic and find its period.

A function f(x) satisfies the functional equation x^(2)f(x)+f(1-x)=2x-x^(4) for all real x.f(x) must be

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

A function f is said to be periodic if it repeats its nature after certain interval and that interval is called period of the function. If T be the period of f(x), then f(x + T) = f(x). For example f(x) = tan x is periodic with period pi . Then find the period of f(x) that satisfies the following condition. (i) f(x + 1) - f(x + 3) = 0 (ii) f(x + 3) + f(x) = 0 (iii) f(x-1) + f(x+3) = f(x+1) + f(x + 5) (iv) f(x + p) = 1+{(1-f(x-p))^(2n+1)}^((1)/(2n+1)), n in N

If f(x) satisfies the relation 2f(x)+(1-x)=x^(2) for all real x, then find f(x) .

f(x)={[x]+[-x], where x!=2 and lambda where If f(x) is continuous at x=2 then,the value of lambda will be

The function f(x) satisfies the equation f(x+1)+f(x-1)=sqrt(3)f(x) .then the period of f(x) is