Question

Let $f:A\to B$ and $g:B\to C$ be two functions and gof $:A\to C$ is defined. Then which of the following statement(s) is/are incorrect?

• A. If gof is into then $g$ must be into.
• B. If gof is onto then $f$ must be onto.
• C. If gof is one-one then $f$ must be one-one.
• D. If gof is bijective then both $f$ and $g$ must be bijective.

Answer 1

Answer: (A), (B), (D)

Note: If f and g are both bijective then gof is also bijective but converse (in general) is not true