If 𝑓(𝑥)=𝑥+9‾‾‾‾‾√ and 𝑔(𝑥)=𝑥2−6, find (𝑓𝑔)(𝑥).

To find the composite function (𝑓𝑔)(𝑥), we need to substitute g(x) into f(x).

Given 𝑓(𝑥)=√(𝑥+9) and 𝑔(𝑥)=𝑥²−6,

First, let's find g(x): g(x) = x² - 6

Now, we substitute g(x) into f(x), replacing every x in f(x) with g(x):

(fg)(x) = f(g(x)) = √(g(x) + 9)

Substitute g(x) = x² - 6 into the equation:

(fg)(x) = √((x² - 6) + 9)

Simplify the equation:

(fg)(x) = √(x² + 3)

So, (𝑓𝑔)(𝑥) = √(x² + 3).