Question

The natural domain of the function (f(x, y) = sqrt{frac{ln(x - 2)}{-1 - y^2}}) is ({(x, y) : x > 2}) ({(x, y) : 2 < x le 3}) ({(x, y) : x > 3}) ({(x, y) : 1 < x le 2}) ({(x, y) : x le 1})

          The natural domain of the function (f(x, y) = sqrt{frac{ln(x - 2)}{-1 - y^2}}) is
({(x, y) : x > 2})
({(x, y) : 2 < x le 3})
({(x, y) : x > 3})
({(x, y) : 1 < x le 2})
({(x, y) : x le 1})

$The natural domain of the function (f(x, y) = sqrtfracln(x - 2)-1 - y^2) is ((x, y) : x > 2) ((x, y) : 2 < x le 3) ((x, y) : x > 3) ((x, y) : 1 < x le 2) ((x, y) : x le 1)$

Added by Eric S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

04/25/2023

Step 1

Since the natural logarithm is only defined for positive arguments, we need $x-2 > 0$. This means that $x > 2$. Show more…

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The natural domain of the function f(x,y) = sqrt(ln(x-2)/(-1-y^2)) is {(x,y) : x > 2} {(x,y) : 2 < x <= 3} {(x,y) : x > 3} {(x,y) : 1 < x <= 2} {(x,y) : x <= 1}