Question

Can someone please help me with problem #9? Please show your work. The answers are either N or O. This is algebra 2 by the way.

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Answer 1

Answer:

$(f \cdot g)(x) = 3x^{\frac{5}{2}}$

Step-by-step explanation:

To find $(f \cdot g)(x)$, which represents the product of functions $f(x)$ and $g(x)$, we simply multiply the expressions for $f(x)$ and $g(x)$.

Given:

• $f(x) = 3x^2$
• $g(x) = \sqrt{x}$

We perform $(f \cdot g)(x)$ as follows:

$(f \cdot g)(x) = f(x) \cdot g(x)$

$(f \cdot g)(x) = (3x^2) \cdot (\sqrt{x})$

Now, let's multiply the terms together:

$(f \cdot g)(x) = 3x^2 \cdot \sqrt{x}$

To simplify, we combine the terms:

$(f \cdot g)(x) = 3x^{\frac{5}{2}}$

So, $(f \cdot g)(x) = 3x^{\frac{5}{2}}$.