If $f(x)=x^2+4x$ and $g(x)=3x-5$ , how do you find $(f(g(x))$ and $g(f(x))$ ?

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If $f(x)=x^2+4x$ and $g(x)=3x-5$ , how do you find $(f(g(x))$ and $g(f(x))$ ?

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Answer 1 · 2015-02-19T13:39:55

It might be better if we think of the functions as having different parameters, so

If $f(a)=a^2+4a$
and $g(b)=3b−5$ ,

then
$f(g(x))$ simply means re-writing the $f(a)$ equation with $a$ replaced by $g(x)$ :
$f(g(x))$
$= (g(x)^2 + 4(g(x))$
$= (3x - 5)^2 + 4(3x -5)$
$= 9x^2 -18x +5$

Similarly
$g(fx))$
$= 3(x^2 + 4x) - 5$ (by replacing $b$ with $f(x)$ )
$= 3x^2 + 12x$

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If $f(x)=x^2+4x$ and $g(x)=3x-5$ , how do you find $(f(g(x))$ and $g(f(x))$ ?

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If $f(x)=x^2+4x$ and $g(x)=3x-5$ , how do you find $(f(g(x))$ and $g(f(x))$ ?