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

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.**

(4.5, 7) (7, 4.5) (0, 3) (-4, 1) (3, 0) (1, -4) (-7, -5) (-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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**Finding inverse functions algebraically**

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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Section 2.8 - Continuity. continuous pt. discontinuity at x = 0 inf. discontinuity at x = 1 pt. discontinuity at x = 3 inf. discontinuity at x = -3 continuous.

Section 2.8 - Continuity. continuous pt. discontinuity at x = 0 inf. discontinuity at x = 1 pt. discontinuity at x = 3 inf. discontinuity at x = -3 continuous.

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