 Inverse Relation: If an relation pairs of element of a of its domain and b of its range pairs b with a. For example: if (a, b) is an ordered pair of a relation then (b, a) is an ordered pair of its inverse  Inverse function: if both a relation and its inverse are functions

 What is the inverse of the given relation? 1) Switch your x & y 1) plot the pts. and rewrite2) switch to (y,x) 3) plot (y, x)

 Change f(x) to y  Switch your x and y  Solve for y  Rewrite as f -1 (x)  Determine if f -1 (x) is a function

Find the inverse function and determine if it’s a function (We will be using the index cards to the first 2 examples)  1. f(x) = 3x + 5  2. f(x) = 6x – 8  3. f(x) = x  4. f(x) = 5 – 2x 2  5. f(x) = 4 – 3x

 Domain: all your x values For any liner, quadratic, cubic, etc (where the exponent is a whole #) your domain is always: all real numbers or (-∞, ∞) If there is an even root (sq. root, 4 th root etc.), you need to determine what value of x will make the expression = 0, that x value is the minimum domain value & will be written as [#, ∞) Examples: use the 5 example we just did

 Range is all the y values - Determine if your function has a minimum or a maximum value (not both) - If there is not just 1 minimum or maximum your range is: all real numbers or (-∞,∞) - If there is just 1 minimum then your range is: [minimum y value, ∞) - If there is just 1 maximum then your range is: (-∞, maximum y value] - examples: let’s look at the 5 we did

 2 ways: You must graph both the relation & its inverse  1 st way: by hand ◦ A) make a table of values (w/ a minimum of 5 points – if linear pick 2 “-”, 0, and 2 “+”, if it’s quadratic find the vertex & then pick 2 the vertex) ◦ B) plot each point and connect 2 nd way: calculator ◦ A) enter both graphs on the calculator ◦ B) sketch what you see, make sure you have accurate points, so you may have to look at the table of values

 If f and f -1 are inverse: (f -1 ˚ f)(x) = x and (f ˚ f -1 )(x) = x for x in the domains of f and f -1 respectively Examples: determine if the functions are inverses 1. f(x) = 10x – 10 and f -1 (x) = x f(x) = 3 – 7x and f -1 (x) = x – 7 3