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)=x2+10x f(x) = x^{2} + 10x g(x)=5x g(x) = \frac{5}{x}

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

To find f(x)g(x) f(x) \cdot g(x) , multiply the expressions for f(x) f(x) and g(x) g(x) : f(x)g(x)=(x2+10x)(5x) f(x) \cdot g(x) = (x^{2} + 10x) \cdot \left( \frac{5}{x} \right)

Step 3: Simplify the expression

Distribute 5x \frac{5}{x} to each term in x2+10x x^{2} + 10x : f(x)g(x)=x25x+10x5x f(x) \cdot g(x) = x^{2} \cdot \frac{5}{x} + 10x \cdot \frac{5}{x} Simplify each term: f(x)g(x)=5x+50 f(x) \cdot g(x) = 5x + 50

Final Answer

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

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