document.write( "Question 115346: State the domain of the following:\r
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document.write( "f(x)= square root (x-8)
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Algebra.Com's Answer #83976 by bucky(2189)![]() ![]() ![]() You can put this solution on YOUR website! You are asked to find the domain of x for the function \n" ); document.write( ". \n" ); document.write( "In order to get a real answer to the square root of a quantity, that quantity must have a \n" ); document.write( "positive value ... including zero. How can you take the square root of a negative number and \n" ); document.write( "get a real number as the answer? You can't because a real number multiplied by itself \n" ); document.write( "only results in a positive number. For example, if you were asked to find the square root \n" ); document.write( "of +9, the answer can only be +3 (because +3 times +3 = +9) or it can be -3 (because -3 \n" ); document.write( "times -3 = +9). So if you were asked to find the square root of -9 you can't because \n" ); document.write( "neither squaring +3 nor squaring -3 will get you -9. \n" ); document.write( ". \n" ); document.write( "So the conclusion is that in this problem the quantity under the radical sign must be \n" ); document.write( "positive which means that it must be greater than or equal to zero. In equation form this \n" ); document.write( "can be written as the inequality: \n" ); document.write( ". \n" ); document.write( " \n" ); document.write( ". \n" ); document.write( "Solve this inequality by adding +8 to both sides to get rid of the -8 on the left side \n" ); document.write( "and the result is: \n" ); document.write( ". \n" ); document.write( " \n" ); document.write( ". \n" ); document.write( "This means that the domain of x is limited to all real values of x that are greater than \n" ); document.write( "or equal to +8 ... all the way toward positive infinity. Another way of expressing this \n" ); document.write( "in algebraic form is: \n" ); document.write( ". \n" ); document.write( " \n" ); document.write( ". \n" ); document.write( "where \n" ); document.write( ". \n" ); document.write( "Hope this helps you to understand the problem a little better. \n" ); document.write( ". \n" ); document.write( " |