Inverse functions - Relations and Functions

Inverse functions

An inverse function is a function that reverses all the operations of another function. Therefore, an inverse function has all the points of another function, except that the x and y values are reversed.


    • a)
      Sketch the graph of the inverse y=f1(x)y = {f^{ - 1}}\left( x \right) in 2 ways:
      i) by reflecting f(x)f\left( x \right) in the line y=xy = x
      ii) by switching the x and y coordinates for each point on f(x)f\left( x \right)
    • b)
      Is f(x)f\left( x \right) a function?
      Is f1(x){f^{ - 1}}\left( x \right) a function?
  • 2.
    Inverse of a Quadratic Function
    Consider the quadratic function: f(x)=(x+4)2+2f(x) = (x+4)^2 + 2
  • 3.
    Determine the equation of the inverse.
    Algebraically determine the equation of the inverse f1(x){f^{ - 1}}\left( x \right), given:
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Inverse functions

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