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**Unformatted text preview: **Lecture 26 1 Lecture 26: (Sec. 5.2) Inverses and Logarithmic Functions ex. Let f ( x ) = x + 1 and let g ( x ) = x 2- 1, x 0. Find: 1) f ( g ( x )) 2) g ( f ( x )) Def. f and g are inverse functions if Lecture 26 2 Properties of Inverse Functions ex. For our functions f ( x ) = x + 1 and g ( x ) = x 2- 1, x 0, find 1) f (3) 2) g (2) We have the following properties: 1) Lecture 26 3 2) 3) Lecture 26 4 To Find the Inverse of a Function: ex. Find f- 1 ( x ) if f ( x ) = x 3 + 2 Lecture 26 5 Logarithmic Functions Def. The inverse of the exponential function y = e x is called the natural logarithmic function . It is written y = and is defined by the following: y = ln x if and only if ex. Evaluate: 1) ln 1 2) ln e Lecture 26 6 ex. Write in exponential form: ln ( 2 5 ) - . 916 ex. Write as a logarithm: e 3 20 . 086 NOTE: Lecture 26 7 Logarithms with other bases Def. The Logarithm of x to the base b : y =log b x if and only if ( x > 0)) ex. Evaluate: 1) log 4 16 2) log 3 ( 1 27 ) 3) log 10 10 Lecture 26...

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