Show that an onto function f - 1- 2- 3 - 1- 2- 3 is always one-one-

F : nbsp;{ 1, 2, 3 }→{ 1, 2, 3 } Since f is onto, all elements of nbsp; { 1, 2, 3 } have unique pre image. Since every element 1, 2, 3 has either of image 1 ...

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Standard XII

Mathematics

Integration by Partial Fractions

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Question

Show that an onto function $f : {1, 2, 3} \to {1, 2, 3}$ is always one-one.

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Solution

$f : {1, 2, 3} \to {1, 2, 3}$
Since $f$ is onto, all elements of ${1, 2, 3}$ have unique pre-image.
Since every element $1, 2, 3$ has either of image $1, 2, 3$
$($ Also, different elements in $f$ have different images $)$
$∴ f$ is one-one.
Hence, proved.

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Integration by Partial Fractions

Standard XII Mathematics

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Show that an onto function f:{1,2,3}→{1,2,3} is always one-one.

f:{1,2,3}→{1,2,3} Since f is onto, all elements of {1,2,3} have unique pre-image. Since every element 1,2,3 has either of image 1,2,3 (Also, different elements in f have different images) ∴f is one-one. Hence, proved.

Show that an onto function $f : {1, 2, 3} \to {1, 2, 3}$ is always one-one.

$f : {1, 2, 3} \to {1, 2, 3}$
Since $f$ is onto, all elements of ${1, 2, 3}$ have unique pre-image.
Since every element $1, 2, 3$ has either of image $1, 2, 3$
$($ Also, different elements in $f$ have different images $)$
$∴ f$ is one-one.
Hence, proved.