Question

For \(f:\mathbb{R}\to\mathbb{R}\) defined by \(f(x)=10x+7\), which function satisfies \(g\circ f=f\circ g=I_R\)?

Options

• \(g(y)=7-10y\)

• \(g(y)=10y+7\)

• \(g(y)=\frac{y+7}{10}\)

• \(g(y)=\frac{y-7}{10}\)

Answer 1

Solving \(y=10x+7\) for \(x\) gives \(x=\frac{y-7}{10}\). Substitution verifies that both \(g(f(x))=x\) and \(f(g(y))=y\), so \(g(y)=\frac{y-7}{10}\).