Questions: If f(x)=x^2+10x and g(x)=5/x, find f(x) · g(x).

Solution Steps

The given functions are: $$f(x) = x^{2} + 10x$$ $$g(x) = \frac{5}{x}$$

To find $f(x) \cdot g(x)$, multiply the expressions for $f(x)$ and $g(x)$: $$f(x) \cdot g(x) = (x^{2} + 10x) \cdot \left( \frac{5}{x} \right)$$

Distribute $\frac{5}{x}$ to each term in $x^{2} + 10x$: $$f(x) \cdot g(x) = x^{2} \cdot \frac{5}{x} + 10x \cdot \frac{5}{x}$$ Simplify each term: $$f(x) \cdot g(x) = 5x + 50$$

Final Answer