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]
Answer:
[tex](gof) (x) =\frac {(x+3)^{\frac{3}{2}}+2}{\sqrt {x + 3}}[/tex]
Step-by-step explanation:
Given : Function [tex]f(x)=\sqrt {x+3}[/tex] and [tex]g(x)=x^2+\frac{2}{x}[/tex]
To find : The value of (gof)(x) ?
Solution :
We know that,
[tex](gof) (x) = g(f (x))[/tex]
Substituting the values,
[tex](gof) (x) = g(\sqrt {x+3})[/tex]
[tex](gof) (x) =(\sqrt {x + 3})^2+ \frac {2} {\sqrt {x + 3}}[/tex]
[tex](gof) (x) =(x + 3) + \frac {2} {\sqrt {x + 3}}[/tex]
[tex](gof) (x) =\frac {(x+3)(\sqrt {x + 3})+2} {\sqrt {x + 3}}[/tex]
[tex](gof) (x) =\frac {(x+3)^{\frac{3}{2}}+2}{\sqrt {x + 3}}[/tex]
