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

Show that the function f:N rarr N given by f(x) = 4x is one-one, but not onto.

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

Show that the function f : R rarr {x in R : -1 < x < 1} defined by f(x) = x/(|x|), x in R is one-one function.

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).

Show that the function f:N rarr N given by f(x) = 5x is one-one but not onto.

Show that if f_1 and f_2 are one-one maps from r to R, then the product. f_1 xx f_2: R rarr R defined by (f_1xx f_2) (x) = f_1 (x) xx f_2(x) need not be one-one.

Show that function defined by f: N rarr N , f (x) = x^3 is one-one but not onto.

Show that an onto function f : {1, 2, 3} rarr {1, 2, 3} is always one-one.