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The range of the function $f(x)=\left\{\begin{array}{cc}4 x-1, & x>3 \\ x^2-2, & -2 \leq x \leq 3 \\ 3 x+4, & x < -2\end{array}\right.$
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The correct answer is:
$\mathbb{R}-(7,11]$
When $x>3,11 < 4 x-1 < \infty$
when $-2 \leq x \leq 3,-2 \leq x^2-2 \leq 7$
when $x < -2,-\infty < (3 x+9) < -2$
Clearly, the given function $f(x)$ have no presence over the interval $(7,11]$ and other than $(7,11], f(x)$ have values corresponding the values of $x$.
Therefore range $(f(x))=R-(7,11]$.
when $-2 \leq x \leq 3,-2 \leq x^2-2 \leq 7$
when $x < -2,-\infty < (3 x+9) < -2$
Clearly, the given function $f(x)$ have no presence over the interval $(7,11]$ and other than $(7,11], f(x)$ have values corresponding the values of $x$.
Therefore range $(f(x))=R-(7,11]$.
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