The function \(f:\mathbb{R}\to\mathbb{R}\) is defined by \(f(x)=x+1\) if \(x<0\) and \(f(x)=x^2\) if \(x\ge0\). What is the correct statement?

Correct answer: (f) is not one-one because the ranges of the two pieces overlap

Step 1: In a piecewise function check the ranges of different pieces. Step 2: \(f\left(-\frac{1}{2}\right)=\frac{1}{2}\) and \(f\left(\frac{1}{\sqrt{2}}\right)=\frac{1}{2}\), while the inputs are different. Step 3: Same value from different pieces breaks injectivity.