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

The function f(x) satisfies the equation f(x + 1) + f(x-1) = sqrt3 f(x) . then the period of f(x) is

If f(2+x)=a+[1-(f(x)-a)^4]^(1/4) for all x in R ,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.

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.

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.

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.