Lesson28

Lesson28 - MA 15200 Lesson 28 Section 4.2 Remember the...

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1 MA 15200 Lesson 28 Section 4.2 Remember the following information about inverse functions. 1. In order for a function to have an inverse, it must be one-to-one and pass a horizontal line test. 2. The inverse function can be found by interchanging x and y in the function’s equation and solving for y . 3. If 1 ( ) , then ( ) f a b f b a  . The domain of f is the range of 1 f and the range of f is the domain of 1 f . 4. The compositions 11 ( ( )) and ( ( )) f f x f f x  both equal x . 5. The graph of 1 f is the reflection of the graph of f about the line yx . Because an exponential function is 1-1 and passes the horizontal line test, it has an inverse. This inverse is called a logarithmic function. I Logarithmic Functions According to point 2 above, we interchange the x and y and solve for y to find the equation of an inverse function. () x f x b exponential function inverse function y xb How do we solve for y ? There is no way to do this. Therefore a new notation needs to be used to represent an inverse of an exponential function, the logarithmic function. Definition of Logarithmic Function For 0 and 0 ( 1) log is equivalent to y b x b b y x x b The function ( ) log b f x x is the logarithmic function with base b . The equation log b is called the logarithmic form and the equation y is called the exponential form. The value of y
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Lesson28 - MA 15200 Lesson 28 Section 4.2 Remember the...

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