Lert `f : X rarr Y` be such that fof = f. Show that f is onto if and only if f is one-one.

Let N rarr N be defined by f (x) = 3x. Show that f is not an onto function.

If f is a function from R rarr R such that f(x) = x^2 , then show that f is not one-one .

Let f : X rarr Y be an invertible function. Show that the inverse of f^–1 is f, i.e. (f^–1)^–1 = f

Let f : N to N : f(x) =2 x for all x in N Show that f is one -one and into.

A function f: R rarr R be defined by f(x) = 5x+6. prove that f is one-one and onto.

Let a function f:R rarr R be defined by f(x) = 3 - 4x Prove that f is one-one and onto.

Let f : A rarr B and g : B rarr C be onto functions, show that gof is an onto function.

If f:R rarr R and f(x)=g(x)+h(x) where g(x) is a polynominal and h(x) is a continuous and differentiable bounded function on both sides, then f(x) is one-one, we need to differentiate f(x). If f'(x) changes sign in domain of f, then f, if many-one else one-one. If f:R rarr R and f(x)=2ax +sin2x, then the set of values of a for which f(x) is one-one and onto is

Show that f : R rarr~ gien f (X) =x^3 is bijective.

Show that f : N rarr N given by : f(x) = {x+ 1, if x is odd x - 1 , if x is even is both one-one and onto.