Question 1073093: f(x)=3x and g(x)=x^2 find g(f(x)) and f(g(x)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! f(x) = 3x
g(x) = x^2
f(g(x)) = 3 * g(x) = 3 * x^2 = 3x^2
g(f(x)) = g(3x) = (3x)^2 = 9x^2
what you are essentially doing is relacing the argument in f(x) with g(x) and replacing the argument in g(x) with f(x).
the argument in f(x) = 3x is x.
the argument in g(x) = x^2 is also x.
when you want to find f(g(x)), you are replacing the argument of x with g(x).
since g(x) is equal to x^2, then the argument in f(x) becomes g(x) and the formula becomes f(g(x)) = 3 * x^2.
the original argument of x was replaced with the new argument of x^2.
likewise, when you want to find g(f(x)), you are replacing the argument of x with f(x). since f(x) is equal to 3x, then the argument in g(x) becomes g(3x) and the formula becomes g(f(x)) = (3x)^2.
in functional notation, the expression in the parentheses is the argument of the function.
you start with the original argument of the function, and then replace that agument with whatever it is you want to evaluate the function against.
for example:
f(x) = x^2
f(3) = 3^2
f(sqrt(y)) = (sqrt(y))^2
f(y) = y^2
f(g(x)) = (g(x))^2
etc......
here's an excellent reference that i just discovered that you might find useful as it explains functional notations in a way that is clear and easy to understand.
https://mathbitsnotebook.com/Algebra1/Functions/FNNotationEvaluation.html
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