Answer:
[tex] (f \cdot g)(x) = 3x^{\frac{5}{2}} [/tex]
Step-by-step explanation:
To find [tex] (f \cdot g)(x) [/tex], which represents the product of functions [tex] f(x) [/tex] and [tex] g(x) [/tex], we simply multiply the expressions for [tex] f(x) [/tex] and [tex] g(x) [/tex].
Given:
- [tex] f(x) = 3x^2 [/tex]
- [tex] g(x) = \sqrt{x} [/tex]
We perform [tex] (f \cdot g)(x) [/tex] as follows:
[tex] (f \cdot g)(x) = f(x) \cdot g(x) [/tex]
[tex] (f \cdot g)(x) = (3x^2) \cdot (\sqrt{x}) [/tex]
Now, let's multiply the terms together:
[tex] (f \cdot g)(x) = 3x^2 \cdot \sqrt{x} [/tex]
To simplify, we combine the terms:
[tex] (f \cdot g)(x) = 3x^{\frac{5}{2}} [/tex]
So, [tex] (f \cdot g)(x) = 3x^{\frac{5}{2}} [/tex].
