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Inverse Functions. Function If for every x there exists at most one y One – to – One Function If for every x there exists at most one y AND for every.

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Presentation on theme: "Inverse Functions. Function If for every x there exists at most one y One – to – One Function If for every x there exists at most one y AND for every."— Presentation transcript:

1 Inverse Functions

2 Function If for every x there exists at most one y One – to – One Function If for every x there exists at most one y AND for every y there exists at most one x Function One – to – One Function NOT One – to – One

3 Only one – to – one functions have inverses GRAPHICALLY One – to – One Function Inverse

4 One – to – One Function Inverse Function and Inverse have Symmetry about the line y = x

5 Find the inverse graph of the function below, if it exists. Since not ONE – TO – ONE, no inverse function exists

6 Find the inverse graph of the function below, if it exists. (-7, -5) (-5, -7) (-4, 1) (1, -4) (0, 3) (3, 0) (7, 4.5) (4.5, 7)

7 Find the inverse graph of the function below, if it exists.

8 Finding inverse functions algebraically

9 PCH ONLY – LOOK AT PROBLEM 68

10 Derivatives of Inverse Functions If f is differentiable at every point on an interval, and f ’ is never zero on the interval, then: is differentiable at every point on the interior of the Interval and its value at the point f(x) is:

11 Find the derivative of the inverse of f(x) = 5 – 4x evaluated at c = ½

12 Find the derivative of the inverse of evaluated at c = 4 Not One-to-One However….One-to-One on [2, 6] which not only includes c = 4, but it also eliminates f ‘ (x) = 0 issue as well Alternative…….

13 Find the derivative of the inverse of evaluated at c = 4

14 Find the derivative of the inverse of at c = 1


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