7.5 Inverse Function

7.5 Inverse Function 3/13/2013

-1 1 3 5 -2 -1 0 1 -2 -1 0 1 -1 1 3 5 What do you notice about the 2 tables (The original function and it’s inverse)? The input of the original function is the output of the inverse and the output of the original function is the input of the inverse.

Notice the graphs of are mirror images of each other along y = x

Inverse Function A function and its inverse function can be described as the "DO" and the "UNDO" functions. Inverse function is written as “f inverse of x” The inverse of a functionis the set of ordered pairs obtained by interchanging the domain(input) and range (output) values in the original function.

The inverse of a functionis the set of ordered pairs obtained by interchanging the domain(input) and range (output) values in the original function. • If then = ? • If then = ? • If and then = ? • Iffind Based on the above definition, answer the following questions. 3 -4 1 5

Steps for finding the inverse of a function: • Replace f(x) with y. • Switch x and y in the original equation. • Solve for y. Replace y with (1) (2) (3) (3)

Find the inverse of the following functions. b.)

7.5 Inverse Function

7.5 Inverse Function

Presentation Transcript

One-to-One Functions; Inverse Function

7.5

7.5

Constant of Variation Direct Variation Function Function Rule Function Notation Inverse variation

The Derivative of Inverse Function

Recall the definition of an inverse function.

Inverse Function Theorem and Implicit Function Theorem

FUNCTIONS – Inverse of a function

2. Inverse functions Inverse relation, Function is a relation

7.5

Finding the Inverse of a Rational Function

The Inverse Cosine Function

Inverse of a function

To find the inverse of a function:

7.5 Roots and Zeros of a Function

Function Inverse

Determine whether the inverse of a function is a function.

6.1 One-to-One Functions; Inverse Function

7.5