Consider functions `f` and `g` such that composite `gof` is defined and is one-one. Are `f `and `g` both necessarily one-one.

Are f and g both necessarily onto, if gof is onto?

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.

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

Show that the function f(x) = 2x+9 is one-one.

Consider the function f(x) = (1-x)/(1+x) . Is f one-one? If yes, find f^-1

A function f : R rarr R is defined by f(x) = 4x^3 +5, x in R examine if f is one-one and onto.

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

Show. that the function f: R rarr R defined by f(x)= (3x-1)/3, x inR is one-one and onto function.

Show that the function f : X -> Y, such that f(x)= 5x + 7 is one-one.