How do you find the compositions given $f(x)=sqrt(x-3)$ , $g(x)=sqrt(x +3)$ ?

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Answer 1 · 2017-05-18T23:29:04

$f(g(x)) = sqrt(sqrt(x + 3) - 3)$

$g(f(x)) = sqrt(sqrt(x - 3) + 3)$

The two possible compositions are $f(g(x))$ and $g(f(x))$ :

$Rightarrow f(g(x)) = f(sqrt(x + 3))$

$Rightarrow f(g(x)) = sqrt(sqrt(x + 3) - 3)$

$and$

$Rightarrow g(f(x)) = g(sqrt(x - 3))$

$Rightarrow g(f(x)) = sqrt(sqrt(x - 3) + 3)$

How do you find the compositions given f(x)=sqrt(x-3)f(x)=sqrt(x-3), g(x)=sqrt(x +3)g(x)=sqrt(x +3)?