6.7 Inverse functions

Presentation Transcript

What is an inverse function?

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

Find an inverse given a table or graph

What is the inverse of the given relation?
Switch your x & y 1) plot the pts.

and rewrite 2) switch to (y,x)

3) plot (y, x)

Finding the inverse of a function

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

examples

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) = x2 + 4
4. f(x) = 5 – 2x2
5. f(x) = 4 – 3x

Determine domain of inverse function

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, 4th 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

Determine the range

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

Graphing

2 ways: You must graph both the relation & its inverse
1st 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 and 2 > the vertex)
B) plot each point and connect

2nd way: calculator