SOLUTION: Given : f(x)=2x^2+2 1. Find the domain of f(x). 2. Find the range of f(x). 3. Find the inverse of f(x). 4. Find the domain of f-1(x). 5. Find

Algebra ->  Inverses -> SOLUTION: Given : f(x)=2x^2+2 1. Find the domain of f(x). 2. Find the range of f(x). 3. Find the inverse of f(x). 4. Find the domain of f-1(x). 5. Find      Log On


   

Question 891757:
Given : f(x)=2x^2+2
1. Find the domain of f(x).

2. Find the range of f(x).

3. Find the inverse of f(x).




4. Find the domain of f-1(x).

5. Find the range of f-1(x).

6. Graph f(x) and f-1(x) on the same plane
7. Which is a function?
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
f(x), no restrictions. ALL REAL Numbers for domain.

Viewing as for standard form, f%28x%29=2%28x-0%29%5E2%2B2 with minimum at y=2.
Range is f%28x%29%3E=2.

f(x) does not really have an inverse; unless you specify for the left and right branches of f around x=0.

LEFT BRANCH OF f:
Domain is -infintity to 0,
Range is from 2 to +infinity.
INVERSE OF LEFT BRANCH of f:
Domain is from 2 to +infinity.
Range is -infinity to 0.
THE ACTUAL FUNCTION OF INVERSE OF LEFT BRANCE OF f:
----This will be the lower branch for y%5E2%2B2=x when solved for y. You want the negative branch.
---- See how "y" and x are switched places.
---- y%5E2=x-2
y=0%2B-+sqrt%28x-2%29
and you need for here, the "minus" branch: f%5E-1%28x%29=-sqrt%28x-2%29.

You can find the inverse for the right branch of f.