document.write( "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? \n" ); document.write( "
Algebra.Com's Answer #366914 by Theo(13342)\"\" \"About 
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you have g(x) = sqrt(-x)
\n" ); document.write( "when y = 3, x = -9
\n" ); document.write( "when y = 2, x = -2
\n" ); document.write( "when y = 1, x = -1
\n" ); document.write( "presumably, you are given the value of g(x) which you also call y.
\n" ); document.write( "that's ok because you would then have y = g(x) = sqrt(-x) which is valid.
\n" ); document.write( "supposed you are first given that y = 3.
\n" ); document.write( "your equation of y = sqrt(-x) becomes:
\n" ); document.write( "3 = sqrt(-x)
\n" ); document.write( "you would square both sides of this equation to get:
\n" ); document.write( "9 = (sqrt(-x))^2 which becomes:
\n" ); document.write( "9 = -x
\n" ); document.write( "you then multiply both sides of the equation by -1 to get:
\n" ); document.write( "-9 = x which is the same as:
\n" ); document.write( "x = -9
\n" ); document.write( "for your information, the square root of (-x) is only imaginary when x is positive.
\n" ); document.write( "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.
\n" ); document.write( "the same process is used to solve for the other values.
\n" ); document.write( "you are given 2 = sqrt(-x)
\n" ); document.write( "squareboth sides to get:
\n" ); document.write( "4 = (sqrt(-x))^2 which becomes:
\n" ); document.write( "4 = -x which then becomes
\n" ); document.write( "x = -4 after multiplying both sides of the equation by -1.
\n" ); document.write( "additional information for you:
\n" ); document.write( "sqrt(-x) is the same as (-x)^(1/2)
\n" ); document.write( "your equation of:
\n" ); document.write( "2 = sqrt(-x) can also be written as:
\n" ); document.write( "2 = (-x)^(1/2)
\n" ); document.write( "square both sides of this equation to get:
\n" ); document.write( "4 = ((-x)^(1/2))^2 which results in:
\n" ); document.write( "4 = (-x)^((1/2)*2) which becomes:
\n" ); document.write( "4 = (-x)^(1) which becomes:
\n" ); document.write( "4 = -x which then becomes:
\n" ); document.write( "x = -4 after multiplying both sides of the equation by -1.
\n" ); document.write( " \n" ); document.write( "
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