Operations with Functions

Operations with Functions

How to solve operations with functions problems: example and its solution.

Example

If f(x) = 2x and g(x) = x^2 - 1, find the domain of each function. 1. (f + g)(x), 2. (f - g)(x), 3. (f*g)(x), 4. (f/g)(x)

Solve the operations between functions
just like operations between polynomials.

x2 + 2x - 1,
-x2 + 2x + 1,
2x3 - 2x2
don't have any excluded values.

So the domains of these functions are 'real numbers'.

x ≠ ±1,
because x = ±1 makes the denominator 0,
which cannot happen.

excluded value (extraneous solution)

So the domain of (f/g)(x) is x ≠ ±1.