If f(x) = 7x + 9 and g(x) `= 7x^(2) - 3`, then (f - g)(x) is equal to

Options

A. 7(x + 1)
B. `7x - 7x^(2) + 12`
C. `7x - 7x^(2) - 12`
D. `7x^(2) + 7x - 12`

Answer

To find \((f - g)(x)\), we start with the given functions:

1. **Identify the functions**:
- \(f(x) = 7x + 9\)
- \(g(x) = 7x^2 - 3\)

2. **Write down the expression for \((f - g)(x)\)**:
\[ (f - g)(x) = f(x) - g(x) \]

3. **Substitute the expressions for \(f(x)\) and \(g(x)\)**:
\[ (f - g)(x) = (7x + 9) - (7x^2 - 3) \]

4. **Distribute the negative sign**:
\[ (f - g)(x) = 7x + 9 - 7x^2 + 3 \]

5. **Combine like terms**:
\[ (f - g)(x) = -7x^2 + 7x + 12 \]

Thus, the final expression for \((f - g)(x)\) is:
\[ (f - g)(x) = -7x^2 + 7x + 12 \]