Let f be a function defined on [a, b] such that f ′(x) `gt` 0, for all x `in` (a, b). Then prove that f is an increasing function on (a, b).

Prove that f(x)=x-sinx is an increasing function.

Let f be a function defined on [0,2]. Then find the domain of function g(x)=f(9x^2-1)

Let f: A to B be a function such that f(A) =B . Then f is called

Let f(x): [0, 2] to R be a twice differenctiable function such that f''(x) gt 0 , for all x in (0, 2) . If phi (x) = f(x) + f(2-x) , then phi is (A) increasing on (0, 1) and decreasing on (1, 2) (B) decreasing on (0, 2) (C) decreasing on (0, 1) and increasing on (1, 2) (D) increasing on (0, 2)

Let f: NvecZ be a function defined as f(x)=x-1000. Show that f is an into function.

Let f: R->R be a differentiable function for all values of x and has the property that f(x)a n df^(prime)(x) has opposite signs for all value of xdot Then, (a) f(x) is an increasing function (b) f(x) is an decreasing function (c) f^2(x) is an decreasing function (d) |f(x)| is an increasing function

Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x for all x in (0,oo) and f(1)=1 , then

Let a function f be defined by f (x) =[x-|x|]/x for xne 0 and f(0)=2 .Then f is :