SOLUTION: Given the equation of the function f(x)=(x-3)^2-5 a)Determine the equation of the inverse relation f^-1(x) b)State the domain and range of f(x) and f^-1(x)

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Given the equation of the function f(x)=(x-3)^2-5 a)Determine the equation of the inverse relation f^-1(x) b)State the domain and range of f(x) and f^-1(x)      Log On


   

Question 1166999: Given the equation of the function f(x)=(x-3)^2-5
a)Determine the equation of the inverse relation f^-1(x)
b)State the domain and range of f(x) and f^-1(x)
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
When input and output are switched for that kind of parabola, domain and range are then switched. You then will have, as inverse, two different functions.

You can begin by x=%28y-3%29%5E2-5
-
x%2B5=%28y-3%29%5E2%5E2
y-3=0%2B-+sqrt%28x%2B5%29

One part of the inverse is y=3%2Bsqrt%28x%2B5%29 and other part of inverse is y=3-sqrt%28x%2B5%29.