f(g(x)) means do g first, then use that output as the input to f. The order is inside out. How functions are written is in ACT Math functions.
Work from the inside
If f(x) = 2x + 1 and g(x) = x², then f(g(3)) is f(9) = 19. g(f(3)) is g(7) = 49. They are not the same. Write the inner result down before you touch the outer function. Notation for a single function, which you need before you compose two, is in function notation.
A function in pieces
If one of the functions is defined differently on different intervals, pick the piece that matches the inner output, not the original x. That case is in piecewise functions. Whether the result is even allowed is a domain question, in domain and range.
The bottom line
Inner function first. Then that number goes into the outer function. f(g(x)) and g(f(x)) are different jobs.
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