let f(x)=1x f(x)=1x and g(x)=x2 +5x.g(x)=x2 +5x. find (f⋅g)(x)(f⋅g)(x)

Can someone help me with this I dont know how to do this

Not sure whether you mean (f*g) or (fºg)

Do you really mean f(x)1x? That's just the same as x. So, I assume you mean f(x) = 1/x. Why some people cannot find the vinculum baffles me.

(f*g)(x) = f*g = (1/x)*(x^2+5x) = (x^2+5x)/x = x+5

(fºg)(x) = f(g) = 1/g = 1/(x^2+5x)

Similarly,
(f/g)(x) = f/g = (1/x)/(x^2+5x) = 1/(x^3+5x^2)

And why do you repeats all the math stuff?

sorry. I meant "virgule" :-)

To find the product of two functions, (f⋅g)(x), you simply need to multiply the two functions together. In this case, we need to find (f⋅g)(x) where f(x) = (1/x) and g(x) = (x^2 + 5x).

To calculate (f⋅g)(x), you substitute g(x) into f(x). Let's simplify this step by step:

1. Start with the function g(x):
g(x) = x^2 + 5x

2. Replace x in g(x) with f(x):
g(f(x)) = (1/x)^2 + 5(1/x)

3. Simplify the square of (1/x):
g(f(x)) = 1/x^2 + 5/x

So, (f⋅g)(x) = 1/x^2 + 5/x