If f: ℝ → ℝ is defined by f(x) = |x|, which statement is correct?
Answer and explanation
Correct answer: It is a function because every x has exactly one image
A function must assign exactly one output to every input in its domain. For every real number x, |x| is a uniquely determined non-negative real number, so f: ℝ → ℝ is indeed a function. It is not required that different inputs have different outputs; that stronger property is injectivity. Since f(2) = f(−2) only shows that the function is not one-one, option A is correct.
Frequently asked questions
What is the correct answer to this question?
It is a function because every x has exactly one image
Why is this the correct answer?
A function must assign exactly one output to every input in its domain. For every real number x, |x| is a uniquely determined non-negative real number, so f: ℝ → ℝ is indeed a function. It is not required that different inputs have different outputs; that stronger property is injectivity. Since f(2) = f(−2) only shows that the function is not one-one, option A is correct.
Which subject and chapter does this question cover?
This is a Class 11 Mathematics question. Chapter: Relations and Functions. Topic: Functions as a special kind of relation.
