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1. If the domain of a function f(x) is the set {10, 20, 30}. What does the information tell you about f-1(x)?

2. If the graph of a function f(x) includes the point (3, 0), what point must the graph of f-1(x) include? Explain.

3.The first term in an arithmetic sequence is 2. The twelfth term is 211. Find the value of n so that an = 135.

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Answer:

  1. the range of f^-1(x) is {10, 20, 30}.

  2. the graph of f^-1(x) will include the point (0, 3)

  3. n = 8

Step-by-step explanation:

1. The domain of a function is the range of its inverse, and vice versa. The range of f^-1(x) is {10, 20, 30}.

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2. See above. The domain and range are swapped between a function and its inverse. That means function point (3, 0) will correspond to inverse function point (0, 3).

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3. The n-th term of an arithmetic sequence is given by ...

  an = a1 +d(n -1)

You are given a1 = 2, a12 = 211, so ...

  211 = 2 + d(12 -1)

  209/11 = d = 19 . . . . . solve the above equation for the common difference

Now, we can use the same equation to find n for an = 135.

  135 = 2 + 19(n -1)

  133/19 = n -1 . . . . . . . subtract 2, divide by 19

  7 +1 = n = 8 . . . . . . . . add 1

135 is the 8th term of the sequence.

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