To find \( f(x) = g(x) - h(x) \), we will first evaluate \( g(x) \) and \( h(x) \).
Step 1: Evaluate \( g(x) \)
The function \( g(x) \) is given by: \[ g(x) = 4^2 - 2 \] Calculating it: \[ g(x) = 16 - 2 = 14 \]
Step 2: Evaluate \( h(x) \)
The function \( h(x) \) is given by: \[ h(x) = x^2 - 3x + 1 \]
Step 3: Substitute \( g(x) \) and \( h(x) \) into \( f(x) \)
Now substituting \( g(x) \) and \( h(x) \) into \( f(x) \): \[ f(x) = g(x) - h(x) = 14 - (x^2 - 3x + 1) \]
Step 4: Simplify \( f(x) \)
Now we can simplify: \[ f(x) = 14 - x^2 + 3x - 1 \] \[ f(x) = -x^2 + 3x + 13 \]
Conclusion
Thus, the function \( f(x) \) is: \[ \boxed{-x^2 + 3x + 13} \]