document.write( "Question 115346: State the domain of the following:\r
\n" ); document.write( "\n" ); document.write( "f(x)= square root (x-8)
\n" ); document.write( "
\n" ); document.write( "

Algebra.Com's Answer #83976 by bucky(2189)\"\" \"About 
You can put this solution on YOUR website!
You are asked to find the domain of x for the function \"f%28x%29+=+sqrt%28x-8%29\"
\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( "\"x+-+8+%3E=0\"
\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( "\"x+%3E=+%2B8\"
\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( "\"%2B8+%3C=+x+%3C+%2Boo\"
\n" ); document.write( ".
\n" ); document.write( "where \"%2Boo\" represents positive infinity.
\n" ); document.write( ".
\n" ); document.write( "Hope this helps you to understand the problem a little better.
\n" ); document.write( ".
\n" ); document.write( "
\n" );