If `f: X -> Y and g: Y -> Z` are two one-one onto mappings then prove that `gof: X -> Z` is also one-one and onto mapping.

If f:X rarr Y and g:Y rarr Z are two one-one onto mappings then prove that gof:X rarr Z is also one-one and onto mapping.

If mapping f:A rarr B is one-one onto,then prove that mapping f^(-1):B rarr A is also one- one onto.

A mapping f: X to Y is one-one, if

A mapping f: X to Y is one-one, if

Give an example of a map Which is not one - one but onto

Let f: A to B and g: B to 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.

Let f: A to B and g: B to 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.

Give an example of a map Which is one - one but not onto

Let f : A rarr B, g : B rarr C be two functions such that gof is one-one and onto. Show that f is one-one and g is onto.

Let f:R->R and g:R->R be two one-one and onto functions such that they are mirror images of each other about the line y=a . If h(x)=f(x)+g(x) , then h(x) is (A) one-one onto (B) one-one into (D) many-one into (C) many-one onto