Composing functions help? :)?

Question

f(x) = 2x-3

g(x) = 3x

find f of g(x) and g of f(x)

also if you could explain how you arrived at the answer that would be very helpful..i'm not sure how to do this at all

Answer 1

(f of g)(x) = f(g(x))

Plug g(x) into the x for f(x),

2(g(x)) - 3 ----> 2(3x) - 3

= 6x - 3  <==== Solution for f(g(x))

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(g of f)(x) = g(f(x))

Plug f(x) into the x for g(x),

3(f(x)) ----> 3(2x - 3)

= 6x - 9 <==== Solution for g(f(x))