Composition of Functions

Composition of functions involves chaining functions together so that the output of one function becomes the input of another. It is denoted $(f \circ g)(x) = f(g(x))$ .

Given

$a(x) = x^2,$
$b(x) = x+3,$

we can evaluate $(a \circ b)(x) = a(x+3) = (x+3)^2$ .

While addition and multiplication of functions is commutative (i.e., $f+g = g+f$ ), the composition of functions is not. Note that $(b \circ a)(x) = b(x^2) = x^2+3$ is not the same as $(a \circ b)(x)$ .

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
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`\boxed{123}`	$\boxed{123}$

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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$