Answer
(a) $g(-1)=2$
(b) $g(x+5)= x^2+12x+38$
(c) $g(-x)=x^2-2x+3$
Work Step by Step
RECALL:
$g(a)$ represents the value of the function $g$ when $x=a$.
Evaluate the function by substituting the given value of $x$.
(a)
Substitute $4$ into $x$ to obtain:
$g(-1) = (-1)^2+2(-1)+3
\\g(-1)=1+(-2)+3
\\g(-1)=-1+3
\\g(-1)=2$
(b)
Substitute $x+5$ into $x$ to obtain:
$g(x+5) = (x+5)^2+2(x+5)+3
\\g(x+5)= x^2+10x+25+2x+10+3
\\g(x+5)= x^2+12x+38$
(c)
Substitute $-x$ into $x$ to obtain:
$g(-x) = (-x)^2+2(-x)+3
\\g(-x) = x^2+(-2x)+3
\\g(-x)=x^2-2x+3$
