How do you find $(f o g) (x)$ $(fog)(x)$ given $f (x) = x^{2} + 7$ $f(x)=x^2+7$ and $g (x) = x - 3$ $g(x)=x-3$ ?

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How do you find $(f o g) (x)$ $(fog)(x)$ given $f (x) = x^{2} + 7$ $f(x)=x^2+7$ and $g (x) = x - 3$ $g(x)=x-3$ ?

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Answer 1 · 2017-03-26T18:09:44

$(f o g) (x)$ $(fog)(x)$ can be written as $f (g (x))$ $f(g(x))$ . I prefer the latter notation, because it better illustrates that you substitute the equivalent of $g (x)$ $g(x)$ for every x that you see in $f (x)$ $f(x)$ .

Explanation:

Given: $f (x) = x^{2} + 7$ $f(x)=x^2+7$ and $g (x) = x - 3$ $g(x)=x-3$

To find $f (g (x))$ $f(g(x))$ , we substitute $x - 3$ $x-3$ for every x that we see in $f (x)$ $f(x)$ :

$f (g (x)) = {(x - 3)}^{2} + 7$ $f(g(x)) = (x-3)^2+7$

Technically, we are done but it is better to simplify the right side:

$f (g (x)) = x^{2} - 6 x + 9 + 7$ $f(g(x)) = x^2-6x+9+7$

$f (g (x)) = x^{2} - 6 x + 16 \leftarrow$ $f(g(x)) = x^2-6x+16 larr$ the answer

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How do you find $(f o g) (x)$ $(fog)(x)$ given $f (x) = x^{2} + 7$ $f(x)=x^2+7$ and $g (x) = x - 3$ $g(x)=x-3$ ?

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How do you find (fog)(x)(fog)(x)(fog)(x) given f(x)=x^2+7f(x)=x2+7f(x)=x^2+7 and g(x)=x-3g(x)=x−3g(x)=x-3?

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How do you find $(f o g) (x)$ $(fog)(x)$ given $f (x) = x^{2} + 7$ $f(x)=x^2+7$ and $g (x) = x - 3$ $g(x)=x-3$ ?