Question

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

Options

• \((f+g)\circ h=f\circ(g+h)\)

• \((f+g)\circ h=f\circ h+g\circ h\)

• \((f+g)\circ h=f\circ h-g\circ h\)

• \((f+g)\circ h=f+g+h\)

Answer 1

For every \(x\in\mathbb{R}\), \(((f+g)\circ h)(x)=f(h(x))+g(h(x))\). This equals \((f\circ h)(x)+(g\circ h)(x)\), proving the identity.