William W. answered • 02/01/19
Experienced Tutor and Retired Engineer
Your question is missing something.
f(x) just represents a function (rule) with the variable x as the independent variable (that means you get to pick what number you want to plug in for x). For example, if the rule is that you will take the number you pick and double it (since x represents the number you pick), then the rule will be 2 times x or 2x. In algebra, we write that as f(x) = 2x [f(x) is pronounced f of x)].
In your case, f(x) = 10x + 7 so the rule says to take the number you pick, multiply it by 10 and add 7. The solution is a set of numbers - if you pick 2, f(x) will be 27 so the ordered pair (2, 27) is one solution. If you pick 1, then f(x) will be 17 making the ordered pair (1, 17) another solution. The set of solutions in this case forms a line.
You may be used to seeing something that says y = 10x + 7. f(x) is just another way of writing y.
As far as the rest of your question involving g(x) and IR, I'm unsure what you mean - there is something missing in the question so I'm unable to help you unless you share the entire question or context.
