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Claire H.

asked • 10/23/16

Finding Domain and Range of a Multivariable Function

for the following function find the domain D and range T and show that for every c ∈ T there exists x,y such that f(x,y) = c. Sketch the Domain.
The following is my own answer but I am unsure if it is correct and was wondering if you could check it for me.
f(x,y) = 8ln(2+x+y2
Domain: {(x,y)∈ R2 : x+y2 > -2}
Assume Range = R
To determin if this is true, for each c ∈ we must find a pair (x,y) such that f(x,y) = c 
f(ec/8-2,0) = 8ln(2+ec/8 - 2 +0) = 8(c/8) = c , therefore c ∈ range and the range of f(x,y) = R
I don't understand what it means when it says sketch the domain?

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