Exercise · ZW-FUNCTION-008 · ★★☆ Intermediate
The function f(x)=x² from ℝ to ℝ is not injective because...
Choose one option.
Show answer
- A. f(1)=f(-1)
Explanation
f(x) = x² is not injective because f(1) = 1 = f(−1) with 1 ≠ −1: two different inputs share the same output. Domain and codomain do exist (they are ℝ).
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.
\[f:A\to B\]
More practice problems: function
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- ZW-FUNCTION-004 Which rule defines a function from ℝ to ℝ?
- ZW-FUNCTION-005 The codomain of f : A → B is...
- ZW-FUNCTION-006 A function is injective if...
- ZW-FUNCTION-007 A function f:A→B is surjective if...
- ZW-FUNCTION-009 Which of these rules defines a function from ℝ to ℝ?