Functions and Their Inverses Essential Questions How do we determine whether the inverse of a function is a function? How do we write rules for the inverses of functions? Holt McDougal Algebra 2 Holt Algebra2

You have seen that the inverses of functions are not necessarily functions. When both a relation and its inverses are functions, the relation is called a one-to-one function. In a one-to-one function, each y-value is paired with exactly one x-value. You can use composition of functions to verify that two functions are inverses. Because inverse functions “undo” each other, when you compose two inverses the result is the input value x.

Determining Whether Functions Are Inverses Determine by composition whether each pair of functions are inverses. Find the composition f (g(x)), then g(f (x)). Substitute x + 1 for x in f. 1 3 Use the Distributive Property. Simplify. Because f (g(x)) ≠ x, f and g are not inverses. There is no need to check g(f(x)).

Determining Whether Functions Are Inverses Determine by composition whether each pair of functions are inverses. Find the composition f (g(x)), then g(f (x)). Because f(g(x)) = g(f (x)) = x for all x but 0 and 1, f and g are inverses.

Determining Whether Functions Are Inverses Determine by composition whether each pair of functions are inverses. Find the composition f (g(x)), then g(f (x)). Because f(g(x)) = g(f (x)) = x, f and g are inverses.

Determining Whether Functions Are Inverses Determine by composition whether each pair of functions are inverses. Find the composition f (g(x)), then g(f (x)). Because f (g(x)) ≠ x, f and g are not inverses. There is no need to check g(f(x)).

Lesson 14.2 Practice B