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

Let f(x)= sin x +ax +b , then which of the following is/are true-

Suppose the function f(x) is defined as follows : f(x)= x(x-1)(x-2)(x-3)...(x-100) Then which one of the following is correct ?

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)

If 3f(x) + 2f(-x) =5(x-2) , state which of the following is the value of f(0) :

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(x) be a differentiable function. If h(x)=(1)/(3) {f(x)}^(3)+{f(x)}^(2)+f(x)+(1)/(3) then which one of the following is correct ?

If f(x)a n dg(x) are two positive and increasing functions, then which of the following is not always true? (a) [f(x)]^(g(x)) is always increasing (b) [f(x)]^(g(x)) is decreasing, when f(x) 1,t h e n[f(x)]^(g(x)) is increasing.

If f'(x)= x and f(1)=3 , find f(x)

Let f:RrarrR be defined as . f(x)={(0, "x is irrational"),(sin|x|,"x is irrational"):} Then which of the following is true?