How Do You Solve Functions?
Expressions, Inverse functions and composite functions. The example below shows three separate functions,  f(x) = x2 - 2x + 4,  f(a) = 5x and g(x) = x - 1. In the first section the value 3 is substituted into the function f(x) = x2 - 2x + 4. The answer is 7. Next, the value -6 is substituted into the function f(x) = x2 - 2x + 4. The answer is 52. The second section shows the composite functions ff(x) and fg(x). In the first part the value 3 is substituted into the composite function ff(x). The answer is 45. Next, the value 3 is substituted into the composite function fg(x). The answer is 10.
The graphic below shows examples of inverse functions. The inverse function of x - 2 is x + 2. The inverse function of 4 + 3x is (x - 4)/3. The inverse function of x² - 2 is √(x + 2).
The image below shows the steps involved when finding the inverse function. This method is known as the function machine method.
What Are Functions Used For?
A function describes a relationship between two values, an input value and an output value. Functions must only have one relationship for each input value as shown below. The domain is a set of values that are allowed to be put into the fuction. The range represents the set of possible results produced when values are input into the function.
There are four types of functions: 1. Constant Function, 2. Linear Function, 3. Quadratic Function and 4. Cubic Function.
There are four types of mappings: one-to-one, many-to-one, one-to-many, and many-to-many. One-many and many-many are not functions.