A composite function is a function that is formed by applying one function to the result of another function.
The composite function of $f$ and $g$ is denoted by $f(g(x))$ or $(f \circ g)(x)$.
Note
The notation $f(g(x))$ is read as " \$f\$ of \$g\$ of \$x\$" or " \$f\$ composed with \$g\$ at \$x\$".
Hint
When working with composite functions, always start with the inner functionand work your way out.
Definition of Composite Functions
The composite function of $f$ and $g$, denoted by $f(g(x))$, is defined as:
$$f(g(x)) = f(g(x))$$
where $g(x)$ is the input to the function $f$.
Self review
1. Let $f(x) = 3x - 2$ and $g(x) = x^2 + 1$. Find $f(g(x))$ and $g(f(x))$. 2. Let $f(x) = \sqrt{x}$ and $g(x) = x^2 - 4$. Find $f(g(x))$ and $g(f(x))$.
Theory of Knowledge
How do composite functions illustrate the idea of layered processesin mathematics? Can you think of real-world examples where one process depends on the output of another?
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Note
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Hint
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Lorem ipsum dolor sit amet, consectetur adipiscing elit.
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Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris.
Duis aute irure dolor in reprehenderit in voluptate velit esse cillum.
