Answer
$g^{-1}(5)$ = 1
Work Step by Step
$g(x) = x^{2} + 4x$, $x\geq2$
Plug in 5 for g(x) (5 is the x value for $g^{-1}(5)$, so it is the y value for g(x))
$5 = x^{2} + 4x$
$0 = x^{2} + 4x - 5$
0 = (x - 1)(x + 5)
x = 1, -5
x = -5 because it is not in the domain of g(x)
x value of g(x) equals the y value of $g^{-1}(x)$
$g^{-1}(5)$ = 1
