Let `f: A to B; g: B to A` be two functions such that `gof = I_A`. Then; f is an injection and g is a surjection.

Let f:A rarr B;g:B rarr A be two functions such that fog=I_(B). Then; f is a surjection and g is an injection.

Let f and g be two functions such that gof=L_(A) and fog=L_(B). Then; f and g are bijections and g=f^(-1)

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.Then which of the following is these

If f: A-A ,g: A-A are two bijections, then prove that fog is an injection (ii) fog is a surjection.

Let f:[0'1] to [-1,1] and g:[-1,1] to [0,2] be two functions such that g is injective and g^(@) f:[0,1] to [0,2] is surjective. Then

If f:A rarr B and g:B rarr C are onto functions show that gof is an onto function.

Let f:A to A and g:A to A be two functions such that fog(x)=gof (x)=x for all x in A Statement-1: {x in A: f(x)=g(x)}={x in A: f(x)=x}={x in A: g(x)=x} Statement-2: f:A to A is bijection.

Let f:A rarr B and g:B rarr C be two functions.Then; if gof is onto then g is onto; if gof is one one then f is one-one and if gof is onto and g is one one then f is onto and if gof is one one and f is onto then g is one one.

If functions f:A to B and g : B to A satisfy gof= I_(A), then show that f is one-one and g is onto.