Let functions $f:\{1,3,4\} →\{1,2,5\}$ and $g:\{1,2,5\} → \{1,3\}$ be defined as $f=\{(1,2),(3,5),(4,1)\}$ and $g = \{(1,3),(2,3),(5,1)\}$ respectively. Then, which one of the following is correct statement for gof?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → gof is onto
$gof(x)=g(f(x))$
so $g(f(1))=g(2)=3$
$g(f(3))=g(5)=1$
$g(f(4))=g(1)=3$
⇒ for every x ∈ co-domain
there exists atleast some y ∈ domain
⇒ $gof$ is ONTO
as $gof(1)=gof(4)$ ⇒ Not One one