Answer:
(f×g)(x) = x +5.
Step-by-step explanation:
Given : f(x)= \(\frac{1}{x}\) and g(x) = x²+5x.
To find : find (f×g)(x).
Solution: We have given f(x)= \(\frac{1}{x}\) and g(x) = x²+5x.
For (f×g)(x) = f(x) g(x) .
Plug the values
(f×g)(x) = \(\frac{1}{x}\) x²+5x.
(f×g)(x) = \(\frac{x^{2}+5x }{x}\)
On taking x common from the numerator
(f×g)(x) = \(\frac{x(x+5)}{x}\).
(f×g)(x) = x +5.
Therefore, (f×g)(x) = x +5.
