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Question
Let A = {x ∈ R : x ≠ 0, −4 ≤ x ≤ 4} and f : A ∈ R be defined by \[f\left( x \right) = \frac{\left| x \right|}{x}\] for x ∈ A. Then th (is
Options
(a) [1, −1]
(b) [x : 0 ≤ x ≤ 4]
(c) {1}
(d) {x : −4 ≤ x ≤ 0}
(e)
{-1,1}
Solution
\[As, \left| x \right| = \binom{x, x \geq 0}{ - x < 0}\]
\[So, f(x) = \frac{x}{\left| x \right|}\]
\[\text{ When x < 0 i . e . x } \in [ - 4, 0)\]
\[f(x) = \frac{x}{- x} = - 1\]
\[\text{ and when } x > 0 i . e . x \in (0, 4]\]
\[f(x) = \frac{x}{x} = 1\]
\[\text{ So, range } (f) = \left\{ - 1, 1 \right\}\]
Notes
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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