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anonymous
 one year ago
How do I algebraically find the domain of sqrt (1  x^2)? (i'll repost as an equation)
I know the answer is [1,1]. But how do I go about solving it algebraically.
anonymous
 one year ago
How do I algebraically find the domain of sqrt (1  x^2)? (i'll repost as an equation) I know the answer is [1,1]. But how do I go about solving it algebraically.

This Question is Closed

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.1set the expression underneath the radical greater or equal to 0 \[1x^{2} \ge 0 \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Is what I have below correct? \[1  x^2 \ge 0 \] \[1 \ge x^2\] \[\sqrt{1}\ge \sqrt{x^2}\] \[\pm1\ge x\]

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.1trying to come up with a good way to explain this, sorry \[1 \ge x^{2}\] results in \[1 \le x \le 1\]

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0Yes, you are correct. √1=√(x²) 1=x x=±1

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1The radicand must be nonnegative, 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
 one year ago
Best ResponseYou've already chosen the best response.1Since 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
 one year ago
Best ResponseYou've already chosen the best response.1Now 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
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