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

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(39615) (Show Source): You can put this solution on YOUR website!
f(x), no restrictions. ALL REAL Numbers for domain.

Viewing as for standard form, with minimum at y=2.
Range is .

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 when solved for y. You want the negative branch.
---- See how "y" and x are switched places.
----

and you need for here, the "minus" branch: .

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