AP EAMCET · Maths · Functions
The real valued function \(f: \mathrm{R} \rightarrow\left[\frac{5}{2}, \infty\right)\) defined by \(f(x)=|2 x+1|+1|x-2|\) is
- A One-one function but not onto
- B Onto function but not one-one
- C Bijection
- D Neither one-one function nor onto
Answer & Solution
Correct Answer
(B) Onto function but not one-one
Step-by-step Solution
Detailed explanation
\(f: \mathbb{R} \rightarrow\left[\frac{5}{2}, \infty\right), f(x)=|2 x+1|+|x-2|\) \(\rightarrow f(x)=\left\{\begin{array}{lc}-3 x+1, & x \lt \frac{-1}{2} \\ x+3, & \frac{-1}{2} \lt x \lt 2 \\ 3 x-1, & x\gt2\end{array}\right.\) Clearly, any horizontal line will cut the graph…
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