Question

Let $A=\{1,2,3\}$ and $B=\{4,5,6\} f: A \rightarrow B$ is a function defined as $f(1)=4, f(2)=5, f(3)=6$. Write down $f^{\prime}$ as a set of ordered pairs.

Answer 1

SOLUTION :  We have $f(1)=4 . f(2)=5$ and $f(3)=6$

$\because \quad$ The image of distinct elements in A are distinct $f$ is one-one

Also every element in $B$ has at least one pre-image

$\because \quad f$ is onto, $f$ is invertible i.e. $f^{-1}$ exists

Now define $f^{-1}: B \rightarrow A$ as

$f^{-1}(4)=1 \because f(1)=4, f^{-1}(5)=2 \text { and } f^{-1}(6)=3 \\$

$\because \quad f^{-1}=\{(4,1),(5,2),(6,3)\}$