Question
Assume that the function
is a one-to-one function.
(a) If f(4)=8, find f^-1(8). your answer is
(b) If f^-1(-9)=-3, find f(-3).
Your answer is
is a one-to-one function.
(a) If f(4)=8, find f^-1(8). your answer is
(b) If f^-1(-9)=-3, find f(-3).
Your answer is
Answers
GPT-4o mini
For a one-to-one function \( f \):
(a) If \( f(4) = 8 \), this means that when the input is 4, the output is 8. The inverse function \( f^{-1} \) takes outputs back to their corresponding inputs. Therefore, since \( f(4) = 8 \), we have:
\[
f^{-1}(8) = 4
\]
(b) If \( f^{-1}(-9) = -3 \), this indicates that when the input is \(-3\), the output is \(-9\). Thus, applying the function \( f \) to \(-3\) gives:
\[
f(-3) = -9
\]
So, the answers are:
(a) \( f^{-1}(8) = 4 \)
(b) \( f(-3) = -9 \)
(a) If \( f(4) = 8 \), this means that when the input is 4, the output is 8. The inverse function \( f^{-1} \) takes outputs back to their corresponding inputs. Therefore, since \( f(4) = 8 \), we have:
\[
f^{-1}(8) = 4
\]
(b) If \( f^{-1}(-9) = -3 \), this indicates that when the input is \(-3\), the output is \(-9\). Thus, applying the function \( f \) to \(-3\) gives:
\[
f(-3) = -9
\]
So, the answers are:
(a) \( f^{-1}(8) = 4 \)
(b) \( f(-3) = -9 \)