# Math Help - compositions with sq roots

1. ## compositions with sq roots

trying to insert f(x)=sq root x-3 into g(x)=sq root x^2+ 3 (GoF and FoG) but not sure how to get rid of the square roots

2. Hello, vinson24!

Given: . $\begin{array}{ccc}f(x)&=& \sqrt{x-3} \\g(x) &=& \sqrt{x^2+ 3} \end{array}$

Find: . $f\circ g\:\text{ and }\:g\circ f$

$f\circ g \;\;=\;\;f(g(x)) \;\;=\;\;f(\sqrt{x^2+3}) \;\;=\;\;\sqrt{\sqrt{x^2+3}-3}$

$g\circ f \;\;=\;\;g(f(x)) \;\;=\;\;g(\sqrt{x-3}) \;\;=\;\;\sqrt{(\sqrt{x-3})^2 + 3} \;\;=\;\;\sqrt{(x - 3) + 3} \;\;=\;\;\sqrt{x}$

Edit: misread the problem . . . corrected now (I hope).
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3. the x^2 + 3 is in a sq root too or does it not matter

4. thanks so much, i didnt think that first one simplified but wasnt quite sure