Math Snap

STEP 1

1. The function $f$ is one-to-one.
2. We are given that $f(9) = 8$.
3. We need to find $f^{-1}(8)$.

STEP 2

1. Understand the definition of a one-to-one function.
2. Use the property of inverse functions.
3. Determine the value of $f^{-1}(8)$.

STEP 3

Understand that a one-to-one function means each output is mapped from a unique input. Therefore, if $f(a) = b$, then $f^{-1}(b) = a$.

STEP 4

Use the property of inverse functions: If $f(a) = b$, then $f^{-1}(b) = a$.

Given $f(9) = 8$, apply the inverse function property:
Since $f(9) = 8$, it follows that $f^{-1}(8) = 9$.
The value of $f^{-1}(8)$ is:
$$\boxed{9}$$