How do you find $g (f (x))$ $g(f(x))$ if $g (x) = x^{2}$ $g(x) = x^2$ and $f (x) = x + 3$ $f(x) = x + 3$ ?

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How do you find $g (f (x))$ $g(f(x))$ if $g (x) = x^{2}$ $g(x) = x^2$ and $f (x) = x + 3$ $f(x) = x + 3$ ?

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Answer 1 · 2018-03-22T01:53:16

Replace all $x$ $x$ 's in $g (x)$ $g(x)$ with the function $f (x)$ $f(x)$ to get
$g (f (x)) = {(x + 3)}^{2}$ $g( f(x) ) = ( x+3 )^2$

Explanation:

$g (f (x))$ $g(f(x))$ means that you replace all $x$ $x$ 's in $g (x)$ $g(x)$ with the function $f (x)$ $f(x)$ . The easiest way to do this is rewrite $g (x)$ $g(x)$ , replacing all $x$ $x$ 's with a blank set of parenthesis, like this -

$g (f (x)) = {()}^{2}$ $g( f(x) ) = ( )^2$

Now place the function $f (x)$ $f(x)$ into the parenthesis.

$g (f (x)) = {(x + 3)}^{2}$ $g( f(x) ) = ( x+3 )^2$

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How do you find $g (f (x))$ $g(f(x))$ if $g (x) = x^{2}$ $g(x) = x^2$ and $f (x) = x + 3$ $f(x) = x + 3$ ?

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How do you find g(f(x))g(f(x))g(f(x)) if g(x) = x^2g(x)=x2g(x) = x^2 and f(x) = x + 3f(x)=x+3f(x) = x + 3?

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How do you find $g (f (x))$ $g(f(x))$ if $g (x) = x^{2}$ $g(x) = x^2$ and $f (x) = x + 3$ $f(x) = x + 3$ ?