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

If f(x)=x^2+10x and g(x)=5/x, find f(x) · g(x).
Transcript text: If $f(x)=x^{2}+10 x$ and $g(x)=\frac{5}{x}$, find $f(x) \cdot g(x)$.
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Solution

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Solution Steps

Step 1: Write down the given functions

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

Step 2: Multiply the functions \( f(x) \) and \( g(x) \)

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

Step 3: Simplify the expression

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

\(\boxed{5x + 50}\)

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