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If the function $f: R \rightarrow R$ is defined by $f(x)=\left\{\begin{array}{l}2 x-3, \text { if } x < -2 \\ x^2-1, \text { if }-2 \leq x \leq 2 \\ 3 x+2, \text { if } x>2\end{array}\right.$ then $\mathrm{f}$ is
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Verified Answer
The correct answer is:
neither injection nor surjection
$f(x)=\left\{\begin{array}{lc}2 x-3, & x < -2 \\ x^2-1, & -2 \leq x \leq 2 \\ 3 x+2, & x>2\end{array}\right.$
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 surjective
$\therefore f(x)$ is neither injective nor surjective.
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 surjective
$\therefore f(x)$ is neither injective nor surjective.
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