Question

If f: A→B and g:B→C are onto , then gof:A→C is:

• A. a bijective function
• B. a many-one and onto function
• C. a many-one and onto function
• D. an into function

Answer 1

The correct option is C

a many-one and onto function

Let c∈C

g:B→C is onto

⇒c∈Chas a pre image

⇒There exists a b ∈B such that g(b) = c

b ∈B and f: A→B is onto

⇒ b∈ B has a pre image

⇒There exists an a ∈A such that f(a) = b

c = g(b) = g[f(a)] = gof (a)

So, c∈Chas a pre image a∈A , such that gof(a) = c

→gof is an onto function