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 sum of the functions \( f(x) \) and \( g(x) \).

Given:
- \( f(x) = 3x + 1 \)
- \( g(x) = x^2 - 1 \)

We need to find \( (f + g)(x) \).

### Step-by-Step Solution:

1. **Write down the functions:**
\[ f(x) = 3x + 1 \]
\[ g(x) = x^2 - 1 \]

2. **Add the two functions:**
\[ (f + g)(x) = f(x) + g(x) \]
Substitute the expressions for \( f(x) \) and \( g(x) \):
\[ (f + g)(x) = (3x + 1) + (x^2 - 1) \]

3. **Combine like terms:**
\[ (f + g)(x) = 3x + 1 + x^2 - 1 \]
Here, the \( +1 \) and \( -1 \) cancel each other out:
\[ (f + g)(x) = x^2 + 3x \]

4. **Final result:**
\[ (f + g)(x) = x^2 + 3x \]

### Conclusion:
The expression for \( (f + g)(x) \) is \( x^2 + 3x \).