Pre-Calc Exam Notes 120

Pre-Calc Exam Notes 120 - Recall that a Function f is...

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120 Chapter 5 Graphing and Inverse Functions §5.3 5.3 Inverse Trigonometric Functions We have briefy mentioned the inverse trigonometric Functions beFore, For example in Section 1.3 when we discussed how to use the a sin 1 , a cos 1 , and a tan 1 buttons on a calculator to ±nd an angle that has a certain trigonometric Function value. We will now de±ne those inverse Functions and determine their graphs. x Domain y Range f y = f ( x ) Figure 5.3.1 Recall that a function is a rule that assigns a single object y From one set (the range ) to each object x From another set (the domain ). We can write that rule as y = f ( x ), where f is the Function (see ²igure 5.3.1). There is a simple vertical rule For determining whether a rule y = f ( x ) is a Function: f is a Function iF and only iF every vertical line intersects the graph oF y = f ( x ) in the xy -coordinate plane at most once (see ²igure 5.3.2). y x y = f ( x ) (a) f is a Function y x y = f ( x ) (b) f is not a Function Figure 5.3.2 Vertical rule For Functions
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Unformatted text preview: Recall that a Function f is one-to-one (oFten written as 1 1) iF it assigns distinct values oF y to distinct values oF x . In other words, iF x 1 n= x 2 then f ( x 1 ) n= f ( x 2 ). Equivalently, f is one-to-one iF f ( x 1 ) = f ( x 2 ) implies x 1 = x 2 . There is a simple horizontal rule For determining whether a Function y = f ( x ) is one-to-one: f is one-to-one iF and only iF every horizontal line intersects the graph oF y = f ( x ) in the xy-coordinate plane at most once (see igure 5.3.3). y x y = f ( x ) (a) f is one-to-one y x y = f ( x ) (b) f is not one-to-one Figure 5.3.3 Horizontal rule For one-to-one Functions IF a Function f is one-to-one on its domain, then f has an inverse function , denoted by f 1 , such that y = f ( x ) iF and only iF f 1 ( y ) = x . The domain oF f 1 is the range oF f ....
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This note was uploaded on 01/21/2012 for the course MAC 1130 taught by Professor Dr.cheun during the Fall '11 term at FSU.

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