If $h(x)=(f-g)(x), f(x)=5x+2$ how do you determine g(x) given $h(x)=sqrt(x-4)+5x+2$ ?

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Answer 1 · 2018-02-27T19:53:08

$g(x) = -sqrt(x-4)$

Firstly, it's important to note that $(f-g)(x)$ is the same thing as $f(x) - g(x)$ .

$h(x) = f(x) - g(x)$

We can substitute the function names out for the actual functions to find our answer.

$sqrt(x-4) + 5x + 2 = 5x + 2 - g(x)$
$sqrt(x-4) + cancel(5x + 2) = cancel(5x + 2) - g(x)$
$sqrt(x-4) = -g(x)$

$g(x) = -sqrt(x-4)$

If h(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)=sqrt(x-4)+5x+2h(x)=sqrt(x-4)+5x+2?