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Triangle Inequality for Functions

​
f(x)
2
x
x
cos(x)
sin(x)
g(x)
2
x
x
cos(x)
sin(x)
Choose functions
f(x)
and
g(x)
and use the two graphs to understand the triangle inequality. In the vector space of square integrable functions, the inner product of the functions
f
and
g
is
〈f,g〉=
1
∫
-1
f(x)g(x)dx
and the norm of
f
is
f=
〈f,f〉
.
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