Inverse functions

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Inverse functions

  1. 1. Inverse functions Does every function have an inverse? No. A function must be 1 to 1 , or pass the horizontal line test in order to have an inverse. PASS FAIL Notation: f 1 or f 1 ( x)
  2. 2. Characteristics of an inverse function • Algebraically – The domains and ranges are switched y1 x2 x1 y2 • Graphically – The graphs are reflections across the line y = x
  3. 3. How to find an inverse function 1. Switch x and y 2. Solve for y Example: x 1 Show that f ( x) 5 x 1 and g ( x) 5 are inverses a) algebraically b ) graphically

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