Suppose that `f(x)f(f(x))=1` and `f(1000)=999` then which of the following is true

If f(x)=x(1-x)^(3) then which of following is true ?

Let f be a real valued function such that for any real x f(15+x)=f(15-x)and f(30+x)=-f(30-x) Then which of the following statements is true ?

Let f(x) be a twice differentiable function for all real values of x and satisfies f(1)=1,f(2)=4,f(3)=9. Then which of the following is definitely true? (a). f''(x)=2AAx in (1,3) (b) f''(x)= 5 for some x in (2,3) (c) f''(x)=3AAx in (2,3) (d) f''(x)=2 for some x in (1,3)

Let f(x) be linear functions with the properties that f(1) le f(2), f(3) ge f(4) " and " f(5)=5. Which one of the following statements is true?

If f ''(x)|le 1 AA x in R, and f (0) =0=f' (0), then which of the following can not be true ?

Let f: R to R be a function defined by f(x)="min" {x+1,|x|+1}. Then, which of the following is true?

If the graph of y=f(x) is symmetrical about the lines x=1a n dx=2, then which of the following is true? (a) f(x+1)=f(x) (b) f(x+3)=f(x) (c) f(x+2)=f(x) (d) None of these

Let f: R->R be a function defined by f(x+1)=(f(x)-5)/(f(x)-3)AAx in R . Then which of the following statement(s) is/are true?

Let f'(sin x)lt0 and f''(sin x) gt0 forall x in (0,(pi)/(2)) and g(x) =f(sinx)+f(cosx) which of the following is true?

Let f:[0,1]rarrR be a function. Suppose the function f is twice differentiable, f(0)=f(1)=0 and satisfies f\'\'(x)-2f\'(x)+f(x) ge e^x, x in [0,1] Which of the following is true for 0 lt x lt 1 ?