Final answer:
To determine the correct function f(x), we use the provided properties and test each option. The correctly described function, adhering to the given properties and the value f(2) = 10, is found to be f(x) = 5 + x. Option D is correct.
Step-by-step explanation:
The student is asking about how to find the function f(x) if given the properties of f(a, b) = f(a) - b and that f(2) = 10. To find the function, we use the given function properties and the known value f(2) = 10 to determine possible forms of the function.
Substitute a with 2 and b with any number, say 0, to get f(2, 0) = f(2) - 0 = 10. This suggests that f(x) has a constant difference from the x value.
Check the given options and substitute x with 2 to see which option yields a function value of 10. Upon substitution, only the option f(x) = x + 5 gives us 2 + 5 = 7, which is incorrect, so we reject this option. Option a is also incorrect since 2 - 5 results in -3. Option c is incorrect as 5 - 2 equals 3. Therefore, the correct function must be option d, f(x) = 5 + x, since 5 + 2 equals 10.
We can confirm our choice by testing the properties again: f(a, b) = f(a) - b = (5 + a) - b = 5 + a - b for option d.