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Functions

Functions. Inverse Functions. Aim: Exchange the y and x variables in an equation in order to reflect an image through the y = x line. Remember. If a graph passes a vertical line test , then it is a. function. 2. Solve the following for y : 2 y + 3 = x.

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Functions

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  1. Functions Inverse Functions

  2. Aim: Exchange the y and x variables in an equation in order to reflect an image through the y = x line. Remember • If a graph passes a verticalline test, then it is a function 2. Solve the following for y: 2y + 3 = x 2y = x - 3 y = x – 3 2 3. Which transformation is illustrated below? reflection

  3. Aim: Exchange the y and x variables in an equation in order to reflect an image through the y = x line. Inverse Functions • When a function receives input, it generates output. • What if we have the output, and would like to find the input of the a function? • In other words, how can we undo a function?

  4. Aim: Exchange the y and x variables in an equation in order to reflect an image through the y = x line. Algebra • Find the inverse function of f(x) = 3x - 2 switch the x and y change f(x)to y get into y = form change y to f-1(x)

  5. Aim: Exchange the y and x variables in an equation in order to reflect an image through the y = x line. Graph • Graph the inverse function of f(x) = 3x - 2 • You have found the inverse if it passes the horizontal line test. = 1x + 2 3 3 f-1(x) = x + 2 3 • Notice the reflection.

  6. Aim: Exchange the y and x variables in an equation in order to reflect an image through the y = x line. Try this … • Find the inverse function of f(x) = x2 y = x2 x = y2 √ √ ±√x = y f-1(x) = ±√x

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