Find of g(f(x)) when f(x)=sqrt(x+3) and g(x)=(x^2+2)/x.
a. g(f(x))=(x^2+2)(sqrt(x+3))/x
b. g(f(x))=(x+5)/(sqrt(x+3))
c. g(f(x))=(x^2+6x+11)/(sqrt(x+3))
d. g(f(x))=(sqrt(((x^2+2)/x)+3)
Every time I work this problem, I get some crazy answer. Can someone please help me?
g(f) = (f^2+2)/f
= ((√x+3)^2+2)/√(x+3)
= (x+5)/√(x+3)
To find g(f(x)), we need to substitute the function f(x) into the function g(x). Let's go step by step:
1. Start with the given function f(x) = sqrt(x + 3) and the function g(x) = (x^2 + 2) / x.
2. Replace x in g(x) with the expression f(x):
g(f(x)) = (f(x)^2 + 2) / f(x)
3. Substitute f(x) with sqrt(x + 3):
g(f(x)) = (sqrt(x + 3)^2 + 2) / sqrt(x + 3)
4. Simplify the numerator:
g(f(x)) = (x + 3 + 2) / sqrt(x + 3)
5. Combine like terms:
g(f(x)) = (x + 5) / sqrt(x + 3)
Therefore, the correct option is b. g(f(x)) = (x + 5) / sqrt(x + 3).