AP EAMCET · Maths · Functions
Let \(A=\{x \in R, x \neq 0,-4 \leq x \leq 4\} \quad\) and \(f: A \rightarrow R\) defined by \(f(x)=\frac{|x|}{x}\) for \(x \in A\). Then, the range of \(f\) is
- A \(\{1,-1\}\)
- B \(\{x: 0 \leq x \leq 1\}\)
- C (1)
- D \(\{x:-4 \leq x \leq 0\}\)
Answer & Solution
Correct Answer
(A) \(\{1,-1\}\)
Step-by-step Solution
Detailed explanation
Since, \(x\) lies between -4 and 4 and \(f(x)=\frac{|x|}{x}\), then \(f(x)\), is either \(-\frac{x}{x}\) or \(\frac{x}{x}\) as \(x < 0\) or \(x \geq 0\) \(\therefore f(x)\), is either -1 or 1 \[ \therefore \quad R=\{1,-1\} \]
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