If `f(x)=x^(1//3)(x-2)^(2//3)` for all x, then the domain of f' 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

If f(x)=sin log((sqrt(4-x^(2)))/(1-x)) , then the domain of f(x) is ….

If f(x)=sin(log)_e{(sqrt(4-x^2))/(1-x)} , then the domain of f(x) is _____ and its range is __________.

"If "f(x)=(x-1)^(4)(x-2)^(3)(x-3)^(2)(x-4), then the value of f'''(1)+f''(2)+f'(3)+f'(4) equals

If f((x+y)/3)=(2+f(x)+f(y))/3 for all x,y f'(2)=2 then find f(x)

If a , b are two fixed positive integers such that f(a+x)=b+[b^3+1-3b^2f(x)+3b{f(x)}^2-{f(x)}^3]^(1/3) for all real x , then prove that f(x) is periodic and find its period.

consider the real function of f(x ) =(x^2 +2x +3)/( x^2 -8x +12) find the domain of f .

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

Let f_1(x)={x, x leq x leq 1 and 1 x gt1 and 0 ,otherwise f_2(x) =f_1 (-x) for all x abd f_3(x)=-f_2(x) for all x and f_4(x)=-f_3(-x) for all x Which of the following is necessarily true?