Answer: It makes the function one-one, allowing the square root to be defined as its inverse.
- A It makes the function onto ℝ, which the unrestricted version fails to be
- B It converts the function into a linear map on that interval
- C It removes the need for the function to be continuous
- D It makes the function one-one, allowing the square root to be defined as its inverse
Correct answer: D. It makes the function one-one, allowing the square root to be defined as its inverse
Explanation: On [0, ∞) the squaring map is strictly increasing hence injective, and with codomain [0, ∞) it is bijective - exactly what defines √x.
Concept context
Types of relations, equivalence classes, one-one and onto functions, composition, and invertible functions