Given $f(x) = 2x^3 + x^2$ and $g(x) = 7x - 2$ how do you find (gf)(3)?

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Answer 1 · 2018-05-23T20:19:47

$g(f(3))=439$

To find $g(f(3))$ , we need to find $g(f(x))$ first.

$g(x)$ is our outside function, so we'll start with that first.

$color(blue)(g(x)=7x-2)$

Wherever we see an $x$ , we'll replace it with $color(red)(f(x))$ . We get

$g(f(x))=color(blue)(7color(red)((2x^3+x^2))-2$

which further simplifies to

$g(f(x))=14x^3+7x^2-2$

To find $g(f(3))$ , we just have to plug $3$ in for $x$ . We get

$g(f(3))=14(3)^3+7(3)^2-2$

$=>=14(27)+7(9)-2$

$=>=378+63-2$

$=>441-2$

$g(f(3))=439$

Hope this helps!

Given f(x) = 2x^3 + x^2f(x) = 2x^3 + x^2 and g(x) = 7x - 2g(x) = 7x - 2 how do you find (gf)(3)?