SOLUTION: a) Sketch the graph of g: x|--> {{{x^2+6x+7}}} b) Explain why g for x(belongs to) ]-(infinity),-3] has an inverse function {{{g^-1}}} c) Find Algebraically, the equation of {

Algebra ->  Graphs -> SOLUTION: a) Sketch the graph of g: x|--> {{{x^2+6x+7}}} b) Explain why g for x(belongs to) ]-(infinity),-3] has an inverse function {{{g^-1}}} c) Find Algebraically, the equation of {      Log On


   

Question 388228: a) Sketch the graph of g: x|--> x%5E2%2B6x%2B7
b) Explain why g for x(belongs to) ]-(infinity),-3] has an inverse function g%5E-1
c) Find Algebraically, the equation of g%5E-1
Thanks :)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
graph%28300%2C300%2C-8%2C8%2C-8%2C8%2C0%2Cx%5E2%2B6x%2B7%29
The domain of g is (-infinity,infinity).
The range of g is [-2,infinity).
.
.
y=x%5E2%2B6x%2B7
Interchange x and y.
x=y%5E2%2B6y%2B7
x=%28y%5E2%2B6y%2B9%29%2B7-9
x=%28y%2B3%29%5E2-2
%28y%2B3%29%5E2=x%2B2
y%2B3=0+%2B-+sqrt%28x%2B2%29
y=-3+%2B-+sqrt%28x%2B2%29
highlight%28g%5E%28-1%29=-3+%2B-+sqrt%28x%2B2%29%29
The domain of g%5E%28-1%29 is [-2,infinity).
The range of g%5E%28-1%29 is (-infinity,infinity).