Let $X = {1, 2, 3, 4}$ .Determine whether $f = {(1, 1), (2, 3), (3, 4), (4, 1)}$ are functions from $X$ to $X$

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Solution

Here,Image of $1$ is $1$

Image of $2$ is $3$

Image of $3$ is $4$

Image of $4$ is $1$

Hence each element has an image.

$∴ f$ is a function.

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Let X={1,2,3,4}.Determine whether f={(1,1),(2,3),(3,4),(4,1)} are functions from X to X

Here,Image of 1 is 1Image of 2 is 3Image of 3 is 4Image of 4 is 1Hence each element has an image.∴f is a function.

Let $X = {1, 2, 3, 4}$ .Determine whether $f = {(1, 1), (2, 3), (3, 4), (4, 1)}$ are functions from $X$ to $X$

Here,Image of $1$ is $1$

Image of $2$ is $3$

Image of $3$ is $4$

Image of $4$ is $1$

Hence each element has an image.

$∴ f$ is a function.