Question

If $f$ and $g$ are functions such that $fog$ is onto then

• A. $f$ is onto
• B. $g$ is onto
• C. $gof$ is onto
• D. Neither $f$ nor $g$ is onto

Answer 1

The correct option is A $f$ is onto

Given that, fog is onto.
$\Rightarrow$ Range(fog(x))$=$Codomain f(g(x))
$\Rightarrow$ Range of fog(x)$=$ Codomain of f(x)...(1)
Since Range of f(x)$\supseteq$ Range of fog(x) and
Range of f(x)$\subseteq$ Codomain of f(x),
Using (1) we get Range of f(x)$=$Codomain of f(x).
Hence, f(x) is onto.