Question

If
g(x) = x2 + 6x
with
x ≥ −3,
find
g−1(55)

I need help solving this problem this is an example but it does not thoroughly is explained. :/

Answer 1

you need x when g(x) = 55
x^2+6x=55
x^2+6x-55 = 0
(x+11)(x-5) = 0

Since the domain is x >= -3, that means that
g^-1(55) = 5

Note that specifying that x >= -3 means we have chosen only one branch of the parabola, whose vertex is at (-3,-9).

Since g(x) = x^2+6x,
x = -3 ±√(g+9)
we choose to use only the
x = -3+√(g+9)
Thus, when g=55, x=-3+√64 = -3+8 = 5