The correct answer is c. x^2 - x + 6. (f+g)(x)= x^2 - x + 6
To find (f+g)(x), add the expressions for f(x) and g(x).
f(x)+g(x)=(x^2 + 1) + (5 − x)
(f + g)(x) = (x^2 + 1) + (5 - x)
Solving the equation:
(f + g)(x) = x^2 + 1 + 5 - x
(f + g)(x) = x^2 - x + 6
Thus, the correct answer is x^2 - x + 6, which corresponds to option c.