Question

For functions \(f,g,h:\mathbb{R}\to\mathbb{R}\), which identity is established for multiplication?

Options

• \((f\cdot g)\circ h=(f\circ h)\cdot(g\circ h)\)

• \((f\cdot g)\circ h=(f\circ h)+(g\circ h)\)

• \((f\cdot g)\circ h=f\cdot g+h\)

• \((f\cdot g)\circ h=f\circ(g\circ h)\)

Answer 1

For every \(x\in\mathbb{R}\), \(((f\cdot g)\circ h)(x)=f(h(x))\cdot g(h(x))\). This is exactly \(((f\circ h)\cdot(g\circ h))(x)\).