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Question
Express the function f : X → R given by f(x) = x3 + 1 as set of ordered pairs, where X = {−1, 0, 3, 9, 7}
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Solution
The function f : X → R is defined by f(x) = x3 + 1, where X = {−1, 0, 3, 9, 7}.
Now,
\[f\left( - 1 \right) = \left( - 1 \right)^3 + 1 = 0\]
\[f\left( 0 \right) = 0^3 + 1 = 1\]
\[f\left( 3 \right) = 3^3 + 1 = 28\]
\[f\left( 7 \right) = 7^3 + 1 = 344\]
\[f\left( 9 \right) = 9^3 + 1 = 730\]
So,
\[f = \left\{ \left( x, f\left( x \right) \right): x \in X \right\} = \left\{ \left( - 1, 0 \right), \left( 0, 1 \right), \left( 3, 28 \right), \left( 7, 344 \right), \left( 9, 730 \right) \right\}\]
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