Let `f : X rarr Y` be invertible, show that f has unique inverse

Let f : X rarr Y be invertible, show that the inverse of f^(-1) = f, i.e., (f^(-1))^(-1) = f .

Let f: R rarr R , where f(x) = sinx , Show that f is into

Let N rarr R be a function defined as f(x) = 4x^2 + 12x +15 Show that f : N rarr S , where, S is the range of f, is invertible. Find the inverse of f.

Consider f : R rarr R given f(x) = 4x + 3. Show that f is invertible. Find the inverse of f.

If f: RrarrR be defined by f(x)=3x+2.Show that f is invertible.Find f^-1:RrarrR .Hence find f^-1(3) and f^-1(0)

Let f: X rarr Y , be a function. Define a relation R in X given by: R={(a, b): f(a)=f(b)} Examine if R is an equivalence relation.

Let f: f (-x) rarr f(x) be a differentiable function. If f is even, then f'(0) is equal to a)1 b)2 c)0 d)-1

Let f : [a, b] rarr R be a function such that for c in (a, b), f'(c) = f''(c) = f'''(c)= f^(iv) (c) = f^(v)(c) = 0 . Then a)f has a local extremum at x = c b)f has neither local maximum nor minimum at x = c c)f is necessarily a constant function d)it is difficult to say whether (a) or (b).

Let A be the set of all 50 students of class X in a school. Let f : A rarr N be function defined by f(x) = roll numbers of the student x. Show that f is one-one but not onto