SOLUTION: given f(x)=2x^2+2 find the domain, range, and inverse of f(x) and f^-1(x) Graph both on the same plane.

Algebra ->  Rational-functions -> SOLUTION: given f(x)=2x^2+2 find the domain, range, and inverse of f(x) and f^-1(x) Graph both on the same plane.       Log On


   

Question 1055355: given f(x)=2x^2+2 find the domain, range, and inverse of f(x) and f^-1(x)

Graph both on the same plane.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Converting to vertex form,
f%28x%29=2%28x-0%29%5E2%2B2
So the domain is all real numbers, the range is [2,infinity)
To get the inverse, use x,y nomenclature,
y=2x%5E2%2B2
Interchange x and y and solve for y.
The new y is the inverse.
x=2y%5E2%2B2
2%5Ey%5E2=x-2
y%5E2=%28x-2%29%2F2
y=0+%2B-+sqrt%28%28x-2%29%2F2%29
f%5E%28-1%29=0+%2B-+sqrt%28%28x-2%29%2F2%29
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