Given that k(x)

Question

is a one-to-one function and k−1(x)
is the inverse of k(x)
, if k−1(12)=115
and k−1(15)=12
, explore the function numerically to determine k(12)
.

Answer 1

To find \( k(12) \) given the information about the inverse function \( k^{-1}(x) \), we can use the properties of inverse functions.

1. We know that if \( k^{-1}(a) = b \), then it follows that \( k(b) = a \).

Given the provided information:

• \( k^{-1}(12) = 115 \) implies that \( k(115) = 12 \).
• \( k^{-1}(15) = 12 \) implies that \( k(12) = 15 \).

Now, based on this second conclusion:

\[ k(12) = 15. \]

Thus, the value of \( k(12) \) is 15.