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

विकल्प

• (a) [1, −1]

• (b) [x : 0 ≤ x ≤ 4]

• (c) {1}

• (d) {x : −4 ≤ x ≤ 0}

   

• (e) 

  {-1,1} 

Answer 1

\[As, \left| x \right| = \binom{x, x \geq 0}{ - x < 0}\]

\[So, f(x) = \frac{x}{\left| x \right|}\]

\[\text{ When x < 0 i . e . x } \in [ - 4, 0)\]

\[f(x) = \frac{x}{- x} = - 1\]

\[\text{ and when }  x > 0 i . e . x \in (0, 4]\]

\[f(x) = \frac{x}{x} = 1\]

\[\text{  So, range } (f) = \left\{ - 1, 1 \right\}\]