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
Hello, vinson24!
Given: .$\displaystyle \begin{array}{ccc}f(x)&=& \sqrt{x-3} \\g(x) &=& \sqrt{x^2+ 3} \end{array}$
Find: .$\displaystyle f\circ g\:\text{ and }\:g\circ f$
$\displaystyle f\circ g \;\;=\;\;f(g(x)) \;\;=\;\;f(\sqrt{x^2+3}) \;\;=\;\;\sqrt{\sqrt{x^2+3}-3} $
$\displaystyle g\circ f \;\;=\;\;g(f(x)) \;\;=\;\;g(\sqrt{x-3}) \;\;=\;\;\sqrt{(\sqrt{x-3})^2 + 3} \;\;=\;\;\sqrt{(x - 3) + 3} \;\;=\;\;\sqrt{x}$
Edit: misread the problem . . . corrected now (I hope).
.