anonymous
  • anonymous
How do I algebraically find the domain of sqrt (1 - x^2)? (i'll re-post as an equation) I know the answer is [-1,1]. But how do I go about solving it algebraically.
Calculus1
chestercat
  • chestercat
See more answers at brainly.com
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this
and thousands of other questions

anonymous
  • anonymous
\[\sqrt{1-x^2}\]
Vocaloid
  • Vocaloid
set the expression underneath the radical greater or equal to 0 \[1-x^{2} \ge 0 \]
anonymous
  • anonymous
Is what I have below correct? \[1 - x^2 \ge 0 \] \[1 \ge x^2\] \[\sqrt{1}\ge \sqrt{x^2}\] \[\pm1\ge x\]

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

Vocaloid
  • Vocaloid
trying to come up with a good way to explain this, sorry \[1 \ge x^{2}\] results in \[-1 \le x \le 1\]
anonymous
  • anonymous
Thanks
SolomonZelman
  • SolomonZelman
Yes, you are correct. √1=√(x²) 1=|x| x=±1
mathstudent55
  • mathstudent55
The radicand must be non-negative, or \(1 - x^2 \ge 0\) To solve this inequality, factor the left side and solve it as an equation: \((1 + x)(1 - x) = 0\) \(1 + x = 0\) or \(1 - x = 0\) \(x = -1\) or \(x = 1\) Now you have 2 points of interest. These two points of interest divide the number line into 3 regions (not counting the points themselves). |dw:1437618309443:dw|
mathstudent55
  • mathstudent55
Since the inequality has the symbol \(\ge\) which contains =, the points of interest are part of the solution, so you put closed dots on them. |dw:1437618438257:dw|
mathstudent55
  • mathstudent55
Now you test each of the three regions to see which ones are part of the solution. To test each region, choose a point in teat region and test is. If the point works, then the entire region works. Let's test -2 \(1 - (-2)^2 \ge 0\) \(1 - 4 \ge 0\) \(-3 \ge 0\) is false, so left of -1 is not part of the solution. Now let's test 0 \(1 - 0^2 \ge 0\) \(1 - 0 \ge 0\) \(1 \ge 0\) is true, so between -1 and 1 is part of the solution. Now let's test 2 \(1 - ^2 \ge 0\) \(1 - 4 \ge 0\) \(-3 \ge 0\) is false, so to the right of 1 is not part of the solution. |dw:1437618822904:dw|

Looking for something else?

Not the answer you are looking for? Search for more explanations.