Given the functions f(x)=x+4f\left(x\right)=\sqrt{x+4}f(x)=x+4 and g(x)=(x−2)2−4g\left(x\right)=\left(x-2\right)^2-4g(x)=(x−2)2−4 find (f∘g)(x)\left(f\circ g\right)\left(x\right)(f∘g)(x) and (g∘f)(x)\left(g\circ f\right)\left(x\right)(g∘f)(x)

( f ∘ g ) ( x ) = x − 2 \left(f\circ g\right)\left(x\right)=x-2 ( f ∘ g ) ( x ) = x − 2 ; ( g ∘ f ) ( x ) = ( x + 4 ) − 4 x + 4 \left(g\circ f\right)\left(x\right)=\left(x+4\right)-4\sqrt{x+4} ( g ∘ f ) ( x ) = ( x + 4 ) − 4 x + 4 <path d="M95,702 c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14 c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54 c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10 s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429 c69,-144,104.5,-217.7,106.5,-221 l0 -0 c5.3,-9.3,12,-14,20,-14 H400000v40H845.2724 s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7 c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z M834 80h400000v40h-400000z">

3. Functions

Function Composition

College Algebra3. FunctionsFunction Composition

Multiple Choice

Given the functions $f\left(x\right)=\sqrt{x+4}$ and $g\left(x\right)=\left(x-2\right)^2-4$ find $\left(f\circ g\right)\left(x\right)$ and $\left(g\circ f\right)\left(x\right)$

$\left(f\circ g\right)\left(x\right)=\sqrt{x-2}$ ; $\left(g\circ f\right)\left(x\right)=\left(x+4\right)-4\sqrt{x+4}$

$\left(f\circ g\right)\left(x\right)=x-2$ ; $\left(g\circ f\right)\left(x\right)=x\left(x+4\right)$

$\left(f\circ g\right)\left(x\right)=x-2$ ; $\left(g\circ f\right)\left(x\right)=4\sqrt{x-4}$

$\left(f\circ g\right)\left(x\right)=x-2$ ; $\left(g\circ f\right)\left(x\right)=\left(x+4\right)-4\sqrt{x+4}$

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Given the functions $f\left(x\right)=\sqrt{x+4}$ and $g\left(x\right)=\left(x-2\right)^2-4$ find $\left(f\circ g\right)\left(x\right)$ and $\left(g\circ f\right)\left(x\right)$

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Given the functions ﻿f(x)=x+4f\left(x\right)=\sqrt{x+4}f(x)=x+4​﻿ and ﻿g(x)=(x−2)2−4g\left(x\right)=\left(x-2\right)^2-4g(x)=(x−2)2−4﻿ find ﻿(f∘g)(x)\left(f\circ g\right)\left(x\right)(f∘g)(x)﻿ and ﻿(g∘f)(x)\left(g\circ f\right)\left(x\right)(g∘f)(x)﻿

Given the functions $f\left(x\right)=\sqrt{x+4}$ and $g\left(x\right)=\left(x-2\right)^2-4$ find $\left(f\circ g\right)\left(x\right)$ and $\left(g\circ f\right)\left(x\right)$