Given the functions:

Question

\[ <br />
f(x) = x^2 + 1 \quad \text{and} \quad g(x) = 5 - x <br />
\]

Calculate \((f+g)(x)\).

A. \(x^2 + x - 4\)
B. \(x^2 + x + 4\)
C. \(x^2 - x + 6\)
D. \(x^2 + x + 6\)

Answer 1

To calculate \((f+g)(x)\), we need to add the two functions \(f(x)\) and \(g(x)\).

Given: \[ f(x) = x^2 + 1 \] \[ g(x) = 5 - x \]

Now, we compute \((f+g)(x)\): \[ (f+g)(x) = f(x) + g(x) \] Substituting the expressions for \(f(x)\) and \(g(x)\): \[ (f+g)(x) = (x^2 + 1) + (5 - x) \]

Now we simplify this expression: \[ (f+g)(x) = x^2 + 1 + 5 - x \] \[ = x^2 - x + 6 \]

Thus, we find that: \[ (f+g)(x) = x^2 - x + 6 \]

Looking at the options provided, the answer is: C. \(x^2 - x + 6\)