# Subtraction of real function from another

We define subtraction of real functions as (f-g)(x) = f(x) - f(x). But I wonder what does (f-g) mean!!! I don't find any meaning in (sin - (square of))(x).
If it really has any meaning then tell with examples.

h = f -g denotes the actual function which takes an element x in the domain (here it's the intersection of the domains of f and g) and outputs f(x) - g(x). This is why we write (f-g)(x) = f(x) - g(x). Remember f and g are functions, not numbers, whereas f(x) and g(x) are real numbers, if f and g are real valued. While it's important to keep in mind the distinction between a function f and the values of its output f(x) (x in the domain of f), it's rather common to write f(x) to denote the function (e.g. among mathematical analysts), usually for convenience.

We define subtraction of real functions as (f-g)(x) = f(x) - f(x). But I wonder what does (f-g) mean!!! I don't find any meaning in (sin - (square of))(x).
If it really has any meaning then tell with examples.

In the example you give (sin - (square of))(x) would equal sin(x) + x^2. It's really just that simple.

HallsofIvy
(sin- square of)(x) is, according to that definition, $sin(x)- square of (x)= sin(x)- x^2$