If f(x) = 3x + 1 and g(x) `= x^(2) - 1`, then (f + g) (x) is equal to

Options

A. `x^(2) +3x`
B. `x^(2) - 3x +2`
C. `x^(2) + 3x + 2`
D. `x^(2) - 3x`

Answer

To solve the problem, we need to find the expression for \((f + g)(x)\) given the functions \(f(x) = 3x + 1\) and \(g(x) = x^2 - 1\).

### Step-by-Step Solution:

1. **Identify the Functions**:
We have:
\[ f(x) = 3x + 1 \]
\[ g(x) = x^2 - 1 \]

2. **Write the Expression for \( (f + g)(x) \)**:
The sum of the functions \(f\) and \(g\) is given by:
\[ (f + g)(x) = f(x) + g(x) \]

3. **Substitute the Functions**:
Substitute the expressions for \(f(x)\) and \(g(x)\) into the equation:
\[ (f + g)(x) = (3x + 1) + (x^2 - 1) \]

4. **Combine Like Terms**:
Now, combine the terms:
\[ (f + g)(x) = 3x + 1 + x^2 - 1 \]
Simplifying this gives:
\[ (f + g)(x) = x^2 + 3x + (1 - 1) \]
\[ (f + g)(x) = x^2 + 3x \]

5. **Final Result**:
Therefore, the expression for \((f + g)(x)\) is:
\[ (f + g)(x) = x^2 + 3x \]