How do you find $(g o f) (x)$ $(gof)(x)$ given $f (x) = - 3 x + 7$ $f(x)=-3x+7$ and $g (x) = x^{2} - 8$ $g(x)=x^2-8$ ?

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How do you find $(g o f) (x)$ $(gof)(x)$ given $f (x) = - 3 x + 7$ $f(x)=-3x+7$ and $g (x) = x^{2} - 8$ $g(x)=x^2-8$ ?

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Answer 1 · 2017-05-20T13:40:52

$(g \circ f) (x) = 9 x^{2} - 42 x + 41$ $(g@f)(x)=9x^2-42x+41$

Explanation:

To make it a bit more obvious what is happening:

Set $f (x) = z = - 3 x + 7$ $f(x)=z=-3x+7$

$g (z) = z^{2} - 8$ $g(z)=z^2-8$

So by substitution:

$(g \circ f) (x) \to g (z) = {(- 3 x + 7)}^{2} - 8$ $(g@f)(x)->g(z)=(-3x+7)^2-8$

$(g \circ f) (x) = 9 x^{2} - 42 x + 49 - 8$ $(g@f)(x)=9x^2-42x+49-8$

$(g \circ f) (x) = 9 x^{2} - 42 x + 41$ $(g@f)(x)=9x^2-42x+41$

Answer 2 · 2018-08-05T01:42:04

$g (f (x)) = {(- 3 x + 7)}^{2} - 8$ $g(f(x))=(-3x+7)^2-8$

Explanation:

We have the composite function $g (f (x))$ $g(f(x))$ . Notice that $f (x)$ $f(x)$ is the inside function, so we can plug this into $g (x)$ $g(x)$ . We get

$f (x) = - 3 x + 7$ $color(steelblue)(f(x)=-3x+7)$

$g (x) = x^{2} - 8$ $color(purple)(g(x)=x^2-8)$

$g (f (x)) = {(- 3 x + 7)}^{2} - 8$ $color(purple)(g(color(steelblue)(f(x)))=(color(steelblue)(-3x+7))^2-8$

Hope this helps!

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How do you find $(g o f) (x)$ $(gof)(x)$ given $f (x) = - 3 x + 7$ $f(x)=-3x+7$ and $g (x) = x^{2} - 8$ $g(x)=x^2-8$ ?

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How do you find (gof)(x)(gof)(x) given f(x)=−3x+7f(x)=-3x+7 and g(x)=x2−8g(x)=x^2-8?

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Explanation:

Explanation:

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How do you find $(g o f) (x)$ $(gof)(x)$ given $f (x) = - 3 x + 7$ $f(x)=-3x+7$ and $g (x) = x^{2} - 8$ $g(x)=x^2-8$ ?