How do you find the compositions given $f(x)+3x-5$ and $g(x)= sqrt(x-2)$ ?

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Answer 1 · 2016-01-03T16:28:22

$(f@g)(x)=3sqrt(x-2)-5$

$(g@f)(x)=sqrt(3x-7)$

By definition, $(f@g)(x)=f[g(x)]$

$=f(sqrt(x-2))$

$=3sqrt(x-2)-5$ .

Similarly, $(g@f)(x)=g[f(x)]$

$=g(3x-5)$

$=sqrt(3x-5-2)$

How do you find the compositions given f(x)+3x-5f(x)+3x-5 and g(x)= sqrt(x-2)g(x)= sqrt(x-2)?