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

Let f: R rarr R and g: R rarr R be two given functions such that f is injective and g is surjective. Then which of the following is injective? a. gof b. fog c. gog d. none of these

Let f : X rarr Y and g : Y rarr Z be two invertible functions. Then gof is also invertible with (gof)^–1 = f^ –1ofg^–1

Let A be a non-empty set and f : A rarr A, g : A rarr A be two functions such that fog = I_A = gof , show that f and g are ijections and that g = f^-1

Show that if f : A rarr B and g : B rarr C are one-one, then gof : A rarr C is also one-one.

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

Let f: A -> B and g : B -> C be two functions and gof: A -> C is define statement(s) is true? a. If gof is one-one, then f anf g both are one-one b. if gof is one-one, then f is one-one c. If gof is a bijection, then f is one-one and g is onto d. If f and g are both one-one, then gof is one-one.

Let f: A rarr B be one-to-one function such that range of f is (b). Determine the number of elements in A.

Let f : X rarr Y be an invertible function. Show that f has unique inverse.

Give examples of two functions f : NrarrN and g : NrarrN such that g o f is onto but f is not onto.

If function f : A rarr B and g : B rar C are defined by : f(x) = sqrtx and g(x) = x^2 respectively, find gof (x).