If $h (x) = (f + g) (x), f (x) = 5 x + 2$ $h(x)=(f+g)(x), f(x)=5x+2$ how do you determine g(x) given $h (x) = x^{2} + 5 x + 2$ $h(x)=x^2+5x+2$ ?

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Answer 1 · 2018-05-16T23:41:40

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

We have:

$h (x) = (f + g) (x), f (x) = 5 x + 2$ $h(x)=(f+g)(x), f(x)=5x+2$

and we seek $g (x)$ $g(x)$ given $h (x) = x^{2} + 5 x + 2$ $h(x)=x^2+5x+2$

We can write

$h (x) = (f + g) (x)$ $h(x) = (f+g)(x)$
$\ \ \ \ \ \ \ = f(x)+g(x)$

So using $f(x)=5x+2$ and $h(x)=x^2+5x+2$ , then:

$h(x) = f(x)+g(x) => x^2+5x+2 = 5x+2 + g(x)$

So then:

$g(x) = (x^2+5x+2) - (5x+2)$
$\ \ \ \ \ \ \ = x^2+5x+2 - 5x-2$
$\ \ \ \ \ \ \ = x^2$

If h(x)=(f+g)(x), f(x)=5x+2h(x)=(f+g)(x),f(x)=5x+2h(x)=(f+g)(x), f(x)=5x+2 how do you determine g(x) given h(x)=x^2+5x+2h(x)=x2+5x+2h(x)=x^2+5x+2?