Question 484152
Of course there is the implied assumption that shoes sizes are linear.
Using the standard y = f(x), x is the shoe size because in the end you are given one such.  y is the length in inches.
Given f(7.5) = 10 and f(11.5) = 11, we see that an increase in x of 4 results in an increase in y of 1.  So the slope of the linear function is 0.25.
One could find f(0) but it would be weird in the shoe store.
So define z = x - 7.5, and w = y - 10.
This does not change the slope.
w = g(z) = 0.25 z
g(9.5 - 7.5) = 0.25 * 2 = 0.5
f(9.5) = 0.5 + 10 = 10.5
Reasonable check: the asked for 9.5 is half way between the given limits, and the "10 1/2" answer is half way between the function limits, so that is linear.