Question

Let $f:B\to C$ and $g:A\to B$ be two functions and let $h=f\circ g$, Given that $h$ is an onto function. Which one of the following is TRUE ?

• A. $f$ and $g$ should both be onto functions
• B. $f$ should be onto but $g$ need not be onto
• C. $g$ should be onto but $f$ not be onto
• D. Both $f$ and $g$ need not be onto

Answer 1

The correct option is B $f$ should be onto but $g$ need not be onto

Consider the arrow diagram shown below:

Here $f$ is onto but $g$ is not onto, yet $h$ is onto.
As can be seen from diagram if $f$ is not onto, $h$ cannot be onto.
$\therefore f$ should be onto, but $g$ need not be onto.
$\therefore$ Answer is (b)