## Key Equation

 Composite function $\left(f\circ g\right)\left(x\right)=f\left(g\left(x\right)\right)\\$

## Key Concepts

• We can perform algebraic operations on functions.
• When functions are combined, the output of the first (inner) function becomes the input of the second (outer) function.
• The function produced by combining two functions is a composite function.
• The order of function composition must be considered when interpreting the meaning of composite functions.
• A composite function can be evaluated by evaluating the inner function using the given input value and then evaluating the outer function taking as its input the output of the inner function.
• A composite function can be evaluated from a table.
• A composite function can be evaluated from a graph.
• A composite function can be evaluated from a formula.
• The domain of a composite function consists of those inputs in the domain of the inner function that correspond to outputs of the inner function that are in the domain of the outer function.
• Just as functions can be combined to form a composite function, composite functions can be decomposed into simpler functions.
• Functions can often be decomposed in more than one way.

## Glossary

composite function
the new function formed by function composition, when the output of one function is used as the input of another