lecture5 - Lecture 5: Inverse Functions, Logarithms...

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Lecture 5: Inverse Functions, Logarithms (Section 1.6) Def. A function f with domain A is called a one-to-one function if ex. f ( x ) = x 2 ± 1 ex. f ( x ) = x 3 6 - ? ± 6 - ? ± Horizontal Line Test
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Inverse Functions Def. Let f be a one-to-one function with domain A and range B . Then its inverse function f ± 1 has domain range and for any y in B , f ± 1 ( y ) = x if and only if f ± 1 ( x ) = y if and only if Inverse relationships f ± 1 ( f ( x ) ) = for every x in A f ( f ± 1 ( x ) ) = for every x in B
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ex. Show that f ( x ) = x 3 + 1 and g ( x ) = 3 p x ± 1 are inverse functions. To ±nd the inverse of a one-to-one function: 1) 2) 3)
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Inverse functions and graphs ex. Given the graph of f ( x ) = x 3 + 1, sketch the graph of the inverse function. 6 - ? ±
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Logarithmic Functions Recall if a > 0 and a 6 = 1, then y = a x is a one-to-one increasing or decreasing function. The inverse of y = a x is the logarithmic function with base a , written Note that y = log a ( x ) if and only if Sketch the graph f ( x ) = a x , a > 1, and its inverse function f ± 1 ( x ) = log a ( x ).
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lecture5 - Lecture 5: Inverse Functions, Logarithms...

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