Algorithm of one-one function

Algorithm to check function is invertible

If f: A->B and g: B->C are one-one functions, show that gof is one-one function.

If f: AvecBa n dg: BvecC are one-one functions, show that gof is one-one function.

If f:A rarr B and g:B rarr C are one-one functions,show that gof is one-one function.

Which of the following is one-one function ?

Statement-1 : If f(x) and g(x) are one-one functions then f(g(x)) and g(f(x)) is also a one-one function. and Statement-2 The composite function of two one-one function may or many not be one-one.

Statement-1 : If f(x) and g(x) are one-one functions then f(g(x)) and g(f(x)) is also a one-one function. and Statement-2 The composite function of two one-one function may or many not be one-one.

A = {1,2} , the number of one - one functions on A to A is ........

Is an identify function one-one function ?

Statement 1: f(x)=x^(3) is a one-one function. Statement 2: Any monotonic function is a one-one function.