16th Edition

ISBN: 9781938168079

Author: Gilbert Strang, Edwin Jed Herman

Publisher: OpenStax

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Textbook Question

Chapter 4, Problem 394RE

For the following exercises, determine whether the statement is true or false. Justify your answer with a proof or a counterexample.

394. The domain of $f ( x , y ) = x 3 sin − 1$ is $x =$ all real numbers, and $− π ≤ y ≤ π$ .

Expert Solution & Answer

To determine

Whether the given statement is true or false, with counterexample.

Answer to Problem 394RE

Thus, the given statement is false.

Explanation of Solution

Given:

Domain of $f(x,y)=x3sin−1(y),x∈R,−π≤y≤π$

Calculation:

As here, $f(x,y)=x3sin−1(y),x∈R,−π≤y≤π$

$x3$ is continuous for all real values, thus its domain is all real values, but the domain of the function $sin−1(y)$ is $−π2≤y≤π2$

Thus, the given statement is false.

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Chapter 4.8, Problem 393E

Chapter 4, Problem 395RE

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For the following exercises, determine whether the statement is true or false. Justify your answer with a proof or a counterexample. 394. The domain of f ( x , y ) = x 3 sin − 1 is x = all real numbers, and − π ≤ y ≤ π .