Find (f*g)(x) when f(x)=sqr x+3/x and g(x)= sqr x+3/2x

Question

A. (f*g)(x)=x^2+6x+9/2x^2
B. (f*g)(x)=sqr x+3/2x^2
C. (f*g)(x)=x+3/2x^2
D. (f*g)(x)=x^2+9/2x^2

Answer 1

To find (f*g)(x), we need to multiply f(x) and g(x).

f(x) = sqrt(x+3)/x
g(x) = sqrt(x+3)/2x

(f*g)(x) = f(x) * g(x)
= (sqrt(x+3)/x) * (sqrt(x+3)/2x)
= (sqrt(x+3) * sqrt(x+3)) / (x * 2x)
= (x+3) / (2x^2)

So, the answer is (f*g)(x) = (x+3) / (2x^2), which is option C.