Question

If f(x) = ||x||, find f(-1/4)

Answer 1

Answer:

• 1/4

Explanation:

• The double bar || || is used to symbolize the norm function.

It is defined as the inner product.

The inner product of x with x is expressed as ||x|| and it is:

• $||x||=\sqrt{<x,x>}=\sqrt{x.x}=\sqrt{x^2}=length-of-x$

Thus:

• $f(-1/4)=||-1/4||=\sqrt{(-1/4)^2}=1/4$