Final answer:
The value of x satisfying the equation 6 + f^{-1}(x - 1) = 8, where f is one-to-one and f(2) = 8, is x = 9. The solution involves isolating f^{-1}(x - 1) and using the property that for a one-to-one function, f^{-1}(f(2)) = 2.
Step-by-step explanation:
The question requires finding a value of x such that the given equation holds true, given that f is a one-to-one function and f(2) = 8. First, we are given:
6 + f-1(x - 1) = 8
We can rearrange this equation to isolate f-1(x - 1) on one side:
f-1(x - 1) = 2
Since f is one-to-one, for each y there is a unique x such that f(x)=y, and since f(2) = 8, then f-1(8) = 2. So, we can set the right side of our equation equal to 8:
x - 1 = 8
Finally, we solve for x to find:
x = 9