Exercise · ZW-FUNCTION-009 · ★★☆ Intermediate
Which of these rules defines a function from \(ℝ\) to \(ℝ\)?
Choose one option.
Show answer
- D. k(x) = x³ + 1
Explanation
\(k(x) = x^3 + 1\) assigns exactly one real value to each \(x\). \(1/x\) is undefined at \(0\), which belongs to \(\mathbb{R}\); \(\sqrt{x}\) does not exist for negative \(x\), and \(\pm\sqrt{x}\) gives two values.
Review the concept: Function
A function f from A to B assigns to each element of A exactly one element of B. A is the domain and B the codomain.
\[f:A\to B\]
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