Answer: 0
Step-by-step explanation:
g(x) = x² + 6x ; x ≥ -3
To find the inverse, swap the x's and y's and solve for "y":
x = y² + 6y
x + 9 = y² + 6y + 9 add 9 to both sides to create a perfect square
x + 9 = (y + 3)²
[tex]+/-\sqrt{x+9}[/tex] = y + 3 take square root of both sides
[tex]-3 +/-\sqrt{x+9}[/tex] = y ; y ≥ -3
g⁻¹(0) = [tex]-3 +/-\sqrt{0+9}[/tex]
= [tex]-3 +/-\sqrt{9}[/tex]
= -3 ± 3
= -3 + 3 , -3 - 3
= 0 , -6
since the restriction is: y ≥ -3, then -6 is not valid
