Asked by Betty
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).
a. Find (f*g)(x)
b. Find the domain and range of (f*g)(x).
Answers
Answered by
Betty
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)
(f*g)(x)=(1/x)(x^2+5x)
Answered by
Damon
but that is
x+5
straight line
domain is all real numbers
range is all real numbers
x+5
straight line
domain is all real numbers
range is all real numbers
Answered by
Betty
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?
(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?
Answered by
Damon
Yes, but you sure made it complicated :)
Answered by
Betty
I tend to do that, thank you!
Answered by
Damon
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
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
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