SOLUTION: 2. f(x)= square root of x-2+5 a. Find the inverse of f(x). Show the process. b. Find the domain of f -1. c. Graph f and f -1 on the same axes. What relationship do you see

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: 2. f(x)= square root of x-2+5 a. Find the inverse of f(x). Show the process. b. Find the domain of f -1. c. Graph f and f -1 on the same axes. What relationship do you see      Log On


   

Question 932963: 2. f(x)= square root of x-2+5
a. Find the inverse of f(x). Show the process.
b. Find the domain of f -1.
c. Graph f and f -1 on the same axes. What relationship do you see between the two graphs?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
2. f%28x%29=+sqrt%28x-2%29%2B5 ...I guess you have this (you didn't tell what is under sqrt exactly)
a. Find the inverse of f(x). Show the process.
f%28x%29=+sqrt%28x-2%29%2B5...f%28x%29=y
y=+sqrt%28x-2%29%2B5...swap x and y
x=+sqrt%28y-2%29%2B5...solve for y
x-5=+sqrt%28y-2%29...raise both sides to the power of 2
%28x-5%29%5E2=+%28sqrt%28y-2%29%29%5E2
x%5E2-10x%2B25=+y-2
x%5E2-10x%2B25%2B2=+y
y=x%5E2-10x%2B27
so, inverse is f%5E-1%28x%29=x%5E2-10x%2B27
b. Find the domain of f -1.
f%5E-1%28x%29=x%5E2-10x%2B27
the domain: all real numbers
(-infinity,infinity)
c. Graph f and f -1 on the same axes. What relationship do you see between the two graphs?
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+30%2Csqrt%28x-2%29%2B5%2C+x%5E2-10x%2B27%29+

they intersect in two points