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Let A = {x ∈ R : x ≠ 0, −4 ≤ x ≤ 4} and f :

Question:

Let $\mathrm{A}=\{x \in \mathrm{R}: x \neq 0,-4 \leq x \leq 4\}$ and $f: \mathrm{A} \in \mathrm{R}$ be defined by $f(x)=\frac{|x|}{x}$ for $x \in \mathrm{A}$. Then th (is

(a) [1, −1]

(b) [x : 0 ≤ x ≤ 4]

(c) {1}

(d) {x : −4 ≤ x ≤ 0}

Solution:

As, $|x|=\left\{\begin{array}{l}x, x \geq 0 \\ -x<0\end{array}\right.$

So, $f(x)=\frac{x}{|x|}$

When $x<0$ i. e. $x \in[-4,0)$

$f(x)=\frac{x}{-x}=-1$

and when $x>0$ i. e. $x \in(0,4]$

$f(x)=\frac{x}{x}=1$

So, range $(f)=\{-1,1\}$

Disclaimer: The question in the book has some error. The solution is created according to the question given in the book.

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