Advanced Algebra Notes Section 6.4: Use Inverse Functions In Chapter 2 we learned that a ___________ is a set of ordered pairs where the domains are mapped to the ranges. An _________________ is where the domain and the ranges of the original relation are switched around to form a new relation. Original RelationInverse Relation (-2, 4), (-1, 2), (0, 0), (1, -2), (2, -4) To find the inverse of a relation that is given to you as a equation, you will switch the ____ and ____ around in the equation and solve for the _____ variable. Example:Find an equation for the inverse relation. 1)y = -3x + 6 relation inverse relation (4, -2), (2, -1), (0, 0), (-2, 1), (-4, 2) xyy x = -3y + 6 x – 6 = -3y

2) Two functions are said to be inverses of each other if ____________ and ____________. The function g is denoted by ______ (read as “f inverse”) if it is an inverse of function f. Example:Verify that f(x) and g(x) are inverse functions. 3), f(g(x)) = xg(f(x)) = x f -1 f(x) & g(x) are inverses.

4., The graphs of the power functions and are shown below. f(x) & g(x) are inverses.

The inverse of and are _____________ across the dotted line _______. We will use the ___________________ to tell if the inverse of a function is itself a function. The graph of can be intersected twice with a horizontal line and that tells us that its inverse is ______ a function. The graph of on the other hand, cannot be intersected twice by a horizontal line so its inverse is a function. Examples: Find the inverse of a function. 5)6., x > 0 reflected y = x (Then switch the x & y variables and graph the inverse.) horizontal line test not

7)Consider the function. Determine whether the inverse of f is a function and then find its inverse. Graph Horizontal line test passes through graph in two places, so the inverse is not a function.