Let a function f:(0,infty) to (0,infty) be defined by f(x) = |1-frac 1 x |. Then f is:

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EEJ MAIN Mathematics QUESTION #7485

Question 1

Let a function \(f:(0,\infty) \to (0,\infty)\) be defined by \(f(x) = |1-\frac{1}{x}|\). Then f is:

Correct Answer Explanation

We have \(f(x) = |1-\frac{1}{x}| = \begin{cases} 1-\frac{1}{x} & \text{if } x>1 \\ \frac{1}{x}-1 & \text{if } 01\) is \([0,1)\), and for \(0