TS EAMCET · Maths · Functions
If the function \(f: R \rightarrow R\) is defined by \(f(x)=\left\{{l}2 x-3, \text { if } x < -2 \ x^2-1, \text { if }-2 \leq x \leq 2 \ 3 x+2, \text { if } x>2\right.\) then \(\mathrm{f}\) is
- A an injection but not a surjection
- B a surjection but not an injection
- C a bijection
- D neither injection nor surjection
Answer & Solution
Correct Answer
(D) neither injection nor surjection
Step-by-step Solution
Detailed explanation
\(f(x)=\left\{\begin{array}{lc}2 x-3, & x < -2 \\ x^2-1, & -2 \leq x \leq 2 \\ 3 x+2, & x>2\end{array}\right.\) Clearly for \(x \in[-2,2]\) \( f(-2)=f(2) \) \(\therefore f(x)\) is not Injective. Also \(y \notin(-7,-1) \cup(3,8)\) i.e. Range \(\neq\) Codomain \(\Rightarrow\) not…
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