Given that f, of, x, equals, x, squared, minus, 4, x, minus, 21f(x)=x

Question

2
−4x−21 and g, of, x, equals, x, minus, 7g(x)=x−7, find left parenthesis, f, minus, g, right parenthesis, left parenthesis, x, right parenthesis(f−g)(x) and express the result as a polynomial in simplest form.

Answer 1

To find \((f - g)(x)\), we need to subtract the function \(g(x)\) from the function \(f(x)\).

1. Define the functions:

   • \( f(x) = x^2 - 4x - 21 \)
   • \( g(x) = x - 7 \)

2. Subtract the functions: \[ (f - g)(x) = f(x) - g(x) \] \[ = (x^2 - 4x - 21) - (x - 7) \]

3. Distribute the negative sign: \[ = x^2 - 4x - 21 - x + 7 \]

4. Combine like terms:

   • Combine \( -4x \) and \( -x \)
   • Combine \( -21 \) and \( +7 \) \[ = x^2 - 5x - 14 \]

5. Final result: Thus, \((f - g)(x) = x^2 - 5x - 14\).

The polynomial in simplest form is: \[ \boxed{x^2 - 5x - 14} \]