If `(x+1/2)+f(x-1/2)=f(x)` for all `x in R,`then the period of f(x) is _____

If f(x+(1)/(2))+f(x-(1)/(2))=f(x) for all x in R then the period of f(x) is 1(b)2(c)3(d)4

Let f(x) be periodic and k be a positive real number such that f(x+k)+f(x)=0 for all x in R. Then the period of f(x) is

If f:R rarr R is a function such that f(5x)+f(5x+1)+f(5x+2)=0, AA x in R , then the period of f(x) is

If f(x)=(3x)/(7)+2 for all x in R , then: f^-1(1)=

Let f be a twice differentiable function defined on R such that f(0) = 1, f'(0) = 2 and f '(x) ne 0 for all x in R . If |[f(x)" "f'(x)], [f'(x)" "f''(x)]|= 0 , for all x in R , then the value of f(1) lies in the interval:

If f(x)in[1,2] where x in R and for a fixed positive real number pf(x+p)=1+sqrt(2f(x)-{f(x)}^(2)) for all x in R then prove that f(x) is a periodic function

Let g(x) =f(x)-2{f(x)}^2+9{f(x)}^3 for all x in R Then

f:RrarrR,f(x)=x^(3)+x^(2)f'(1)+xf''(2)+f'''(3)" for all "x in R. The value of f(1) is

If f(x)=(1)/(3){f(x+1)+(5)/(f(x+2))} and f(x)>0 foe all x in R, then lim_(x rarr oo)f(x) is