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Published byKeeley Weakley Modified over 2 years ago

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Inverse Functions

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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

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

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

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

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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)

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

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Finding inverse functions algebraically

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PCH ONLY – LOOK AT PROBLEM 68

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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:

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

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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…….

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

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Find the derivative of the inverse of at c = 1

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