Little help with function definitions/notation

cabang

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Feb 21, 2020
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Greetings! It has been so many years since I had calculus that I'm struggling to understand notation like this:

1582301110215.png

What do the math lines mean, in english?
Is gi(x) a series of functions g(x), which are simply numbered 1-m (as in, g1(x), g2(x), g3(x), etc) Or does it mean something else?
(same goes for hj(x)

What does "subject to" mean? Does it mean we for f(x) we can only choose values of x that also satisfy a separate function, g(x) <= 0?
What is the last line, the capital X? Does 'e' mean that x is a member of the larger set X? Or something else?

If I can get my notation straightened out I'll be able to understand so many more of these kinds of math statements. I understand how to do the calculations, just forgot my notation conventions! Wondering if there is a resource that explains notation in one place; I could dig through many textbook chapters to find where different symbols are introduced and explained.

thanks!
 
X is a set of numbers that appears to be unknown as of yet.<=That is not true--see @Dr. Peterson's post below.

[MATH]{x}\in{X}[/MATH] means that x is a member of X.
 
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