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).

6 answers

I know how to set up the problem, but I don't know where to go from there.

(f*g)(x)=(1/x)(x^2+5x)
but that is
x+5
straight line

domain is all real numbers
range is all real numbers
So just to be sure...

(f*g)(x)=(1/x)*x(x+5) - factor the expression, (x^2+5x)
(f*g)(x)=(x(x+5))/x - multiply the two expressions
(f*g)(x)=x+5 - the x/x cancel out leaving x+5

Right?
Yes, but you sure made it complicated :)
I tend to do that, thank you!
The point is that even x^2/x
would have a zero in the denominator as x --->0
BUT
(x/x) x = x, like period. The top goes to zero at exactly the same rate as the bottom, so the expression is really 1 x