Addition and Subtraction of F x^2+x-4 f(x)=x^2+1 g(x)=5-x (f+g)(x)= x^2+x-4 x^2+x+4 x^2-x+6 x^2+x+6 (f-g)(x)= x^2+x+4 x^2-x+6 x^2+x+6

To find the addition and subtraction of the given functions, we need to perform the operations on the corresponding terms of the functions.<br /><br />For addition, we add the corresponding terms of the functions:<br />$(f+g)(x) = f(x) + g(x)$<br /><br />Substituting the given functions, we have:<br />$(f+g)(x) = (x^{2}+1) + (5-x)$<br /><br />Simplifying the expression, we get:<br />$(f+g)(x) = x^{2} - x + 6$<br /><br />Therefore, the correct answer for $(f+g)(x)$ is $x^{2} - x + 6$.<br /><br />For subtraction, we subtract the corresponding terms of the functions:<br />$(f-g)(x) = f(x) - g(x)$<br /><br />Substituting the given functions, we have:<br />$(f-g)(x) = (x^{2}+1) - (5-x)$<br /><br />Simplifying the expression, we get:<br />$(f-g)(x) = x^{2} + x - 4$<br /><br />Therefore, the correct answer for $(f-g)(x)$ is $x^{2} + x - 4$.