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When working with functions it helps to look at a formula like this as a pattern. What this equation tells us is: "The function g takes its input, which we'll call "x" and it will square it, then multiply that by 3 and then add 3 to that." The function g, as defined above, will square, multiply by 3 and add 2 to any input you give it!
g(x+a) means the input is x+a. And what will g do to its input? It will square it, multiply by 3 and add 2!
which simplifies as follows:
For g(x+a) - g(x) we substitute the expressions above:
(