Conceptual Compression Math Example 4

Follow the full solution, then compare it with the other examples linked below.

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The notation

f \circ g

(function composition) compresses which idea? Evaluate

(f \circ g)(x)

when

f(x) = x^2

and

g(x) = x+1

1
Compressed idea: apply $g$ first, then apply $f$ to the result: $(f \circ g)(x) = f(g(x))$ .
2
Compute: $g(x) = x+1$ . Then $f(g(x)) = f(x+1) = (x+1)^2 = x^2+2x+1$ .

Answer

(f \circ g)(x) = x^2+2x+1

Function composition notation

f \circ g

compresses the idea of sequential function application. The order matters:

f \circ g \ne g \circ f

in general.

About Conceptual Compression

The cognitive process of packaging a multi-step procedure or idea into a single mental object that can be manipulated as a unit.

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