Find (g o f)(x) when f(x)= sqrtx+3 and g(x)= x^2+2/x
To find (g o f)(x), we need to substitute the expression for f(x) into g(x).
First, substitute f(x) into g(x):
g(f(x)) = (f(x))^2 + 2/f(x).
Next, substitute the expression for f(x) into g(f(x)):
g(f(x)) = (sqrt(x) + 3)^2 + 2/(sqrt(x) + 3).
Simplify the expression:
g(f(x)) = (x + 6sqrt(x) + 9) + 2/(sqrt(x) + 3).
Thus, (g o f)(x) = (x + 6sqrt(x) + 9) + 2/(sqrt(x) + 3).
To find (g o f)(x), first we need to substitute the function f(x) into the function g(x).
(g o f)(x) = g(f(x))
We are given f(x) = sqrt(x+3) and g(x) = (x^2 + 2)/x.
Substituting f(x) into g(x), we have:
(g o f)(x) = g(f(x)) = g(sqrt(x+3))
Now, we substitute f(x) = sqrt(x+3) into g(x) = (x^2 + 2)/x:
(g o f)(x) = g(f(x)) = (f(x)^2 + 2)/f(x)
Replacing f(x) with its value we have:
(g o f)(x) = g(f(x)) = ((sqrt(x+3))^2 + 2)/(sqrt(x+3))
Simplifying further:
(g o f)(x) = g(f(x)) = (x + 3 + 2)/(sqrt(x+3))
Therefore, (g o f)(x) = (x + 5)/(sqrt(x+3))
To find (g o f)(x), we need to perform the operation g(f(x)). First, let's substitute the given functions into the expression g(f(x)) and simplify.
Given that f(x) = √(x+3) and g(x) = (x^2+2)/x, we have:
(g o f)(x) = g(f(x))
Substituting f(x) = √(x+3) into g(x), we get:
g(f(x)) = [(f(x))^2 + 2]/f(x)
Now, substitute f(x) = √(x+3) into the expression:
g(f(x)) = [ (√(x+3))^2 + 2]/√(x+3)
Simplifying, we can square the square root:
g(f(x)) = [(x+3) + 2]/√(x+3)
g(f(x)) = [x + 5]/√(x+3)
Therefore, (g o f)(x) = [x + 5]/√(x+3).