Let f(x)= 1/x and g(x)=x^2+5x.
a. Find (f*g)(x).
b. Find the domain and range of (f*g)(x).
(f*g)(x) = f(g(x)) = 1/(x^2 + 5x).
Note that f(g(0)) is undefined, so the domain is all real x except for x=0.
The graph below should help you determine the range:
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