# SOLUTION: g(x) = sqrt( -x) I know that that is an imaginary number. I understand that when y = 3, then x = -9. When y = 2, then x = -4, when y = 1, then x = -1. But what is the algebraic

Algebra ->  Algebra  -> Radicals -> SOLUTION: g(x) = sqrt( -x) I know that that is an imaginary number. I understand that when y = 3, then x = -9. When y = 2, then x = -4, when y = 1, then x = -1. But what is the algebraic       Log On

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 Question 568317: g(x) = sqrt( -x) I know that that is an imaginary number. I understand that when y = 3, then x = -9. When y = 2, then x = -4, when y = 1, then x = -1. But what is the algebraic process to get those neg x values?Answer by Theo(3504)   (Show Source): You can put this solution on YOUR website!you have g(x) = sqrt(-x) when y = 3, x = -9 when y = 2, x = -2 when y = 1, x = -1 presumably, you are given the value of g(x) which you also call y. that's ok because you would then have y = g(x) = sqrt(-x) which is valid. supposed you are first given that y = 3. your equation of y = sqrt(-x) becomes: 3 = sqrt(-x) you would square both sides of this equation to get: 9 = (sqrt(-x))^2 which becomes: 9 = -x you then multiply both sides of the equation by -1 to get: -9 = x which is the same as: x = -9 for your information, the square root of (-x) is only imaginary when x is positive. when x is negative, the square root of (-x) becomes the square root of a positive number because minus a negative number results in a positive number. the same process is used to solve for the other values. you are given 2 = sqrt(-x) squareboth sides to get: 4 = (sqrt(-x))^2 which becomes: 4 = -x which then becomes x = -4 after multiplying both sides of the equation by -1. additional information for you: sqrt(-x) is the same as (-x)^(1/2) your equation of: 2 = sqrt(-x) can also be written as: 2 = (-x)^(1/2) square both sides of this equation to get: 4 = ((-x)^(1/2))^2 which results in: 4 = (-x)^((1/2)*2) which becomes: 4 = (-x)^(1) which becomes: 4 = -x which then becomes: x = -4 after multiplying both sides of the equation by -1.