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We can combine functions using addition, subtraction, multiplication, and division. Here are examples of what that may look like.

Let

The sum f + g looks like :

The difference f - g looks like:

The product fg looks like:

The quotient f/g looks like:

The domain for each of these functions consists of all real numbers that are the common domains of f and g. The only exception is the quotient of two functions, you must remember that the denominator cannot be zero!

Source: Blitzer - PreCalculus 4e

An example on how to find the difference of two functions.

An example on how to find the difference of two functions.

EDIT: I made a mistake when writing the answer, can you spot it?

An example on how to find the product of two functions.

An example on how to find the quotient of two functions.