DERIVATIVES OF INVERSE FUNCTIONS GIFT 2004



DERIVATIVES OF INVERSE FUNCTIONS GIFT 2004

1. Let [pic] and let [pic] denote the inverse of [pic]. Then [pic] is equal to:

[pic]

2. Let [pic] and let [pic] denote the inverse of [pic]. Then [pic] is equal to:

[pic]

3. Let [pic] Find the value of [pic] at x = 2.

[pic]

4. Let [pic] and let [pic] denote the inverse of [pic]. Then [pic] is equal to:

[pic]

5. If [pic] and [pic], then calculate: [pic]

[pic]

6. If [pic] then [pic]

[pic]

C 2004 Reardon Inverse Gifts, Inc.

7. Let [pic] and let [pic] be the inverse function of [pic] What is the value of [pic]

[pic]

8. Let [pic] and let [pic] be the inverse function of [pic] What is the value of [pic]

[pic] does not exist

E) [pic] cannot be determined from the given information

9. The following table shows the values of differentiable functions [pic]

|x |[pic] |[pic] |[pic] |[pic] |

|1 |2 |[pic] |[pic] |5 |

|2 |3 |1 |0 |4 |

|3 |4 |2 |2 |3 |

|4 |6 |4 |3 |[pic] |

If [pic] then [pic] equals

[pic]

10. The following table shows the values of differentiable functions [pic]

|x |[pic] |[pic] |[pic] |[pic] |

|[pic] |[pic] |[pic] |[pic] |6 |

|0 |1 |[pic] |3 |5 |

|1 |2 |3 |4 |4 |

|2 |3 |4 |7 |3 |

If [pic] then [pic] equals

[pic]

C 2004 Reardon Inverse Gifts, Inc.

11. Let [pic] and let [pic] denote the inverse of [pic]. Then [pic] is equal to:

[pic]

12. Let [pic] and let [pic] denote the inverse of [pic]. Then [pic] is equal to:

[pic]

13. Let [pic], and let [pic] be the inverse function of [pic] What is the value of [pic]

[pic]

14. Let [pic] Find the value of [pic] at x = 13.

[pic]

15. If [pic] [pic] Compute [pic]

[pic]

Answers (most of them should be correct, I hope ( )

1. B 2. C 3. D 4. C 5. D 6. D

7. B 8. B 9. E 10. E 11. A 12. D

13. A 14. A 15. C

C 2004 Reardon Inverse Gifts, Inc.

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