AP EAMCET · Maths · Functions
If the function \(f: R \rightarrow R\) is defined by \(f(x)=x|x|\), then .
- A \(f\) is one-one but not onto
- B \(f\) is onto but not one-one
- C \(f\) is both one-one and onto
- D \(f\) is neither one-one nor onto
Answer & Solution
Correct Answer
(C) \(f\) is both one-one and onto
Step-by-step Solution
Detailed explanation
Given, \(f(x)=x|x|=\left\{\begin{array}{l}x(x), x \geq 0 \\ x(-x), x According to the graph, domain of \(f(x)=\) Range of \(f(x)=R\) \(\therefore\) Range \(=\) Codomain \(=R\) \(\Rightarrow f(x)\) is an onto function. If a line parallel to…
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