To find \((f \cdot g)(x)\), we need to multiply the functions \(f(x)\) and \(g(x)\).
Given:
- \(f(x) = x^2 + 1\)
- \(g(x) = x - 2\)
The product of the two functions is given by:
\[ (f \cdot g)(x) = f(x) \cdot g(x) \]
Substituting the expressions we have:
\[ (f \cdot g)(x) = (x^2 + 1)(x - 2) \]
Now, we can multiply the terms:
\[ (f \cdot g)(x) = x^2 \cdot (x - 2) + 1 \cdot (x - 2) \]
This expands to:
\[ = x^3 - 2x^2 + x - 2 \]
So, the final result for \((f \cdot g)(x)\) is:
\[ (f \cdot g)(x) = x^3 - 2x^2 + x - 2 \]