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7.4 inverse functions
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7.4 inverse functions

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  • 1. 7.4 Inverse Functions
  • 2. Inverse Relations Remember, a relation is a mapping of input values to output values. An inverse relation maps the outputs back onto the inputs. (The domain and range switch.) Its graph is a reflection of the original relation over the line y = x.
  • 3. Finding an Inverse Relation1. Switch x and y.2. Solve for y.Example: Find the inverse of y = 2x - 4
  • 4. Your Turn! Find the inverse of
  • 5. Inverse Functions If both the original relation and its inverse are functions, they are inverse functions. Functions f and g are inverses if: f(g(x)) = x and g(f(x)) = x Function g is then called f-1 (read “f inverse”)
  • 6. Verifying Inverse Functions Show that Example:Verify thatare inverses.
  • 7. Your Turn! Verify that are inverses.
  • 8. Inverses of Nonlinear Functions f(x) = x2 g(x) = x3 + 2 x = y2The inverse of f(x) = x2 is not a function.If we restrict the domain of f(x) to one side, (say x 0 or x 0 ) then it is.
  • 9. Finding an Inverse Power Function We still switch x and y, then solve for y. Example: Find the inverse of f(x) = x2, x 0
  • 10. Your Turn!  Find the inverse of f(x) = x5
  • 11. Horizontal Line Test Used to determine if the inverse of f is a function. If a horizontal line crosses f more than once, then f inverse is not a function.
  • 12. Finding an Inverse Function Example: For the function determine if the inverse is a function, then find the inverse.
  • 13. Your Turn! For the function determine whether the inverse is a function and find the inverse.