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Find (gof)(x) when f(x)=sqrt x+3 and g(x)= x^2+2/x
4 months ago
Q:
Find (gof)(x) when f(x)=sqrt x+3 and g(x)= x^2+2/x
Accepted Solution
A:
For this case we have the following functions:[tex]f (x) = \sqrt {x + 3}\\g (x) = x ^ 2 + \frac {2} {x}[/tex]We must find [tex](g_ {0} f) (x)[/tex].For definition we have to:[tex](g_ {0} f) (x) = g (f (x))[/tex]So:[tex]g (f (x)) = (\sqrt {x + 3}) ^ 2+ \frac {2} {\sqrt {x + 3}}\\g (f (x)) = (x + 3) + \frac {2} {\sqrt {x + 3}}[/tex]Answer:[tex](g_ {0} f) (x) = (x + 3) + \frac {2} {\sqrt {x + 3}}[/tex]