# Function composition

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If f and g are functions, then we may evaluate the function g on an input x to produce an output y, written ${\displaystyle y=g(x)}$: we then take y as the input to f to produce a further output z, written ${\displaystyle z=f(y)}$. The composite function that takes the initial input x to the final output z is the composite function, written ${\displaystyle z=f(g(x))}$.