Answer
$g(-1) = 2$
$g(x+5) = x^{2} + 12x + 38$
$g(-x) = x^{2} -2x + 3$
Work Step by Step
$g(x) = x^{2} + 2x + 3$
$g(-1) = (-1)^{2} + 2(-1) + 3$
$= 1 - 2 + 3$
$= -1 + 3$
$= 2$
$g(x+5) = (x+5)^{2} + 2(x+5) + 3$
$= [x(x+5)+5(x+5)] + 2x + 10 + 3$
$= x^{2} + 10x + 25 + 2x + 10 + 3$
$= x^{2} + 12x + 38$
$g(-x) = (-x)^{2} + 2(-x) + 3$
$= x^{2} -2x + 3$
