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Home » Let f = {(1, 1), (2, 3), (0, –1), (–1, –3)} be a function from Z to Z defined by f(x) = ax + b, for some integers a, b. Determine a, b.
Let f = {(1, 1), (2, 3), (0, –1), (–1, –3)} be a function from Z to Z defined by f(x) = ax + b, for some integers a, b. Determine a, b.
CBSE | Class 11 | Maths | Miscellaneous Exercise | NCERT | Relations and Functions
Let f = {(1, 1), (2, 3), (0, –1), (–1, –3)} be a function from Z to Z defined by f(x) = ax + b, for some integers a, b. Determine a, b.

Given,

    \[f\text{ }=\text{ }\left\{ \left( 1,\text{ }1 \right),\text{ }\left( 2,\text{ }3 \right),\text{ }\left( 0,\text{ }\text{ }1 \right),\text{ }\left( \text{ }1,\text{ }\text{ }3 \right) \right\}\]

What’s more, the capacity characterized as, f(x) = hatchet + b

For

    \[\left( 1,\text{ }1 \right)\in f\]

We have,

    \[f\left( 1 \right)\text{ }=\text{ }1\]

Along these lines,

    \[a\text{ }\times \text{ }1\text{ }+\text{ }b\text{ }=\text{ }1\]

    \[a\text{ }+\text{ }b\text{ }=\text{ }1\text{ }\ldots \text{ }.\text{ }\left( I \right)\]

What’s more, for

    \[\left( 0,\text{ }\text{ }1 \right)\in f\]

We have

    \[f\left( 0 \right)\text{ }=\text{ }\text{ }1\]

    \[a\text{ }\times \text{ }0\text{ }+\text{ }b\text{ }=\text{ }\text{ }1\]

    \[b\text{ }=\text{ }\text{ }1\]

On subbing

    \[b\text{ }=\text{ }\text{ }1\]

in (I), we get

    \[a\text{ }+\text{ }\left( \text{ }1 \right)\text{ }=\text{ }1\Rightarrow a\text{ }=\text{ }1\text{ }+\text{ }1\text{ }=\text{ }2.\]

Along these lines, the upsides of an and b are 2 and – 1 individually.

i

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