Question

Let \(f:A\to B\) and \(g:B\to C\) be functions. Which expression defines the composition of \(f\) and \(g\)?

Options

• \((g\circ f)(x)=g(x)-f(x)\), for all \(x\in C\)

• \((g\circ f)(x)=f(x)+g(x)\), for all \(x\in A\)

• \((g\circ f)(x)=g(f(x))\), for all \(x\in A\)

• \((g\circ f)(x)=f(g(x))\), for all \(x\in B\)

Answer 1

The composition is defined by \((g\circ f)(x)=g[f(x)]\). Thus, \(f\) is applied first and its output is then used as the input of \(g\).