Find (g•f)(x) when f(x)=sqrt x+3 and g(x)=x^2+2/x
To find (g•f)(x), we need to find the composition of the two functions f(x) and g(x).
First, let's find f(g(x)). We can substitute g(x) into f(x):
f(g(x)) = sqrt(g(x)) + 3
Now let's find g(f(x)). We can substitute f(x) into g(x):
g(f(x)) = (f(x))^2 + 2/f(x)
Substituting the given functions into these equations, we have:
f(g(x)) = sqrt((x^2+2)/x) + 3
g(f(x)) = ((sqrt(x) + 3))^2 + 2/(sqrt(x) + 3)
Therefore, the expressions (g•f)(x) and (f•g)(x) are:
(g•f)(x) = sqrt((x^2+2)/x) + 3
(f•g)(x) = ((sqrt(x) + 3))^2 + 2/(sqrt(x) + 3)