If f = {(1,3) (2,1) (3,4) (4,2)} and g = {(1,2) (2,3) (3,4) (4,1)} then find n(fog)

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Solution

The correct option is C 4
we can find $n (f o g)$ by finding the range of the domain of $f$
In $(1, 3)$ as the range $3$ is mapped to $4$ in $g$ , the ordered pair here for $f o g$ is $(1, 4)$
In $(2, 1)$ as the range $1$ is mapped to $2$ in $g$ , the ordered pair here for $f o g$ is $(2, 2)$
In $(3, 4)$ as the range $4$ is mapped to $1$ in $g$ , the ordered pair here for $f o g$ is $(3, 1)$
In $(4, 2)$ as the range $2$ is mapped to $3$ in $g$ , the ordered pair here for $f o g$ is $(4, 3)$
As we have $4$ ordered pairs for $f o g$ , we have $n (f o g) = 4$

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