If F of X is defined by the ordered pairs (4, 10), (6, 15), (10, 6), and (15, 4), what is F inverse of 6?

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Multiple Choice

If F of X is defined by the ordered pairs (4, 10), (6, 15), (10, 6), and (15, 4), what is F inverse of 6?

To determine F inverse of 6, we first need to understand what the inverse of a function means. The inverse function essentially reverses the roles of inputs and outputs in the original function. For the original function F of X, the pairs given are (x, F(x)). This means that: - F(4) = 10 - F(6) = 15 - F(10) = 6 - F(15) = 4 Now, to find F inverse, we switch the x and y values of these pairs. Thus, we have: - F inverse(10) = 4 - F inverse(15) = 6 - F inverse(6) = 10 - F inverse(4) = 15 We are specifically looking for F inverse of 6. According to our switched pairs, F inverse of 6 corresponds to the output of F for the input that originally yielded 6. From the pair (10, 6), we see that when the input is 10, the output is 6. Thus, it follows that F inverse of 6 is 10, confirming that this choice is indeed the correct answer.

To determine F inverse of 6, we first need to understand what the inverse of a function means. The inverse function essentially reverses the roles of inputs and outputs in the original function. For the original function F of X, the pairs given are (x, F(x)). This means that:

  • F(4) = 10

  • F(6) = 15

  • F(10) = 6

  • F(15) = 4

Now, to find F inverse, we switch the x and y values of these pairs. Thus, we have:

  • F inverse(10) = 4

  • F inverse(15) = 6

  • F inverse(6) = 10

  • F inverse(4) = 15

We are specifically looking for F inverse of 6. According to our switched pairs, F inverse of 6 corresponds to the output of F for the input that originally yielded 6. From the pair (10, 6), we see that when the input is 10, the output is 6.

Thus, it follows that F inverse of 6 is 10, confirming that this choice is indeed the correct answer.

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