f(x)=x^2+1 g(x)=5-x (f+g)(x)= x^2+x-4 x^2+x+4 x2-x+6 x^2+x+6

To find $(f+g)(x)$, we need to add the functions $f(x)$ and $g(x)$ together.<br /><br />Given:<br />$f(x) = x^2 + 1$<br />$g(x) = 5 - x$<br /><br />$(f+g)(x) = f(x) + g(x)$<br /><br />Substitute the given functions:<br />$(f+g)(x) = (x^2 + 1) + (5 - x)$<br /><br />Combine like terms:<br />$(f+g)(x) = x^2 - x + 6$<br /><br />Therefore, the correct answer is:<br />$x^2 - x + 6$