Algebra 2 6-6 Independent Practice: Function Operations

Error Analysis: Your friend used some simple functions and found the following to be true for particular functions f and g and concluded that function composition is commutative.

Give an example to show that your friend is mistaken.

Define each of the following in your counterargument:

• a specific function f(x)

• a specific function g(x)

• the composition of functions (f \circ g)(x)

• the composition of functions (g \circ f)(x)

Note: To form a counterexample, (f \circ g)(x) should not equal (g \circ f)(x).

Open-Ended: List two functions f and g such that, for all real numbers x f(g(x))=x.

HINT: Consider simple functions that include inverse operations.

Remember that you can use the ⊕ button to add Math.

Reflection: Math Success