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Chapter 7, Harder Questions, Answers

Q2

A functional is a function of a function. Explore the concept of a function of a
functional.
If a function is a rule that converts a number into a number, and a functional is a
rule that converts a function into a number [1], then a function of a functional (call it
a 2-functional) should be a rule that converts a functional into a number:

functionfðxÞ¼x^3

rule: cube thenumberx

number¼ 2 #!

X^3

8

functionalF½ðxފ¼

Ð 2

0 fðxÞdx

rule: integrate thefunction f(x)between zero and 2

function¼x^3 ####!

Ð^2

0

fðxÞdx

x^4

4

2

0

¼ 4

Answers 639