# Triangle Inequality for Functions

Triangle Inequality for Functions

Choose functions and and use the two graphs to understand the triangle inequality. In the vector space of square integrable functions, the inner product of the functions and is and the norm of is .

f(x)

g(x)

f

g

〈f,g〉=f(x)g(x)dx

1

∫

-1

f

f=

〈f,f〉