Question

Let \(f\) be the signum function and \(g(x)=\lfloor x\rfloor\). What are \((g\circ f)(\frac12)\) and \((f\circ g)(\frac12)\), respectively?

Options

• \(0,0\)

• \(0,1\)

• \(1,0\)

• \(1,1\)

Answer 1

Since \(\frac12>0\), \(f(\frac12)=1\), and therefore \((g\circ f)(\frac12)=g(1)=1\). Also, \(g(\frac12)=0\), so \((f\circ g)(\frac12)=f(0)=0\).