MHT CET · Maths · Functions
\(f: R \rightarrow R\), then \(f(x)=x|x|\) will be
- A many-one-onto
- B one-one-onto
- C many-one-into
- D one-one-into
Answer & Solution
Correct Answer
(B) one-one-onto
Step-by-step Solution
Detailed explanation
Given, \(f: R \rightarrow R, \quad f(x)=x|x|\)
Redefined the function,
\(
f(x)=\left\{\begin{aligned}
-x^{2}, & x < 0 \\
0, & x=0 \\
x^{2}, & x>0
\end{aligned}\right.\)
The graph of \(f(x)\) shows that it is a bijective (one-one-onto) function.
Redefined the function,
\(
f(x)=\left\{\begin{aligned}
-x^{2}, & x < 0 \\
0, & x=0 \\
x^{2}, & x>0
\end{aligned}\right.\)
The graph of \(f(x)\) shows that it is a bijective (one-one-onto) function.
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