What do you notice about this new relation?

Solve each equation for the given variable. 1. in terms of b 5. in terms of r 3. in terms of m 2. in terms of r in terms of x 4. Do Now Please

xf(x) xg(x)

Example 2

Example 3 Page 254 Prob

Example 4 Find the inverse of f(x) = 7 x -1

Example 5

Example 6 Page 254 Prob

1:1 Functions Functions 1:1 Functions are a subset of Functions. They are special functions where for every x, there is one y, and for every y, there is one x. Relations Reminder: The definition of function is, for every x there is only one y. Inverse Functions are 1:1 Equations

Horizontal Line Test b and c are not one-to-one functions because they don’t pass the horizontal line test. Which ones are one-to- one functions? How do you know?

Example 7 Graph the following function and tell whether it has an inverse function or not.

Example 8 Graph the following function and tell whether it has an inverse function or not. Page 254 Prob

A function and it’s inverse graphed on the same axis. Page 241 Prob

Example 9 If this function has an inverse function, then graph it’s inverse on the same graph.

Example 10 If this function has an inverse function, then graph it’s inverse on the same graph.

Example 11 If this function has an inverse function, then graph it’s inverse on the same graph. Page 241 Prob

Applications of Inverse Functions The function given by f (x)=5/9x+32 converts x degrees Celsius to an equivalent temperature in degrees Fahrenheit. a. Is f a one-to-one function? Why or why not? b. Find a formula for f -1 and interpret what it calculates. F = f (x) = 5/9 x + 32 is 1 to 1 because it is a linear function. The Celsius formula converts x degrees Fahrenheit into Celsius. Replace the f(x) with y Solve for y, subtract 32 Multiply by 9/5 on both sides Page prob

(a) (b) (c) (d) (c)

(a) (b) (c) (d) (a) Review Time!!! Practice Plus on page 241 Prob