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now in this lesson were going to talk about composite functions so lets say that f of x is equal to 3x minus 4 and that g of x lets say its equal to x squared minus three what is f of g notice that this is different from f times g if you see a closed circle its multiplication its 3x minus 4 times x squared minus 3. but if you see like an open circle what it means is its a composite function one function is inside of another g is inside of f so this is equivalent to f of g of x so how can we find f of g of x well lets replace g g is x squared minus three and notice that x squared minus three is inside of f so were going to have to replace x with x squared minus 3. so this is going to be 3 times x squared minus 3 minus 4. so now lets distribute the 3. so thats 3x squared minus 9. minus four which is three x squared minus thirteen now what about g of f how can we find the value of g of f so this time f is inside of g so you can write it like this thats an equivalent expression
