document.write( "Question 398046: What is the domain of the function: sqrt(x(x-7)). Write the answer in interval notation. \n" ); document.write( "

Algebra.Com's Answer #282057 by dnanos(83) $\"\"$ $\"About$

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x(x-7) must have positive values, or zero, in order the square root of it to be a real number.
\n" ); document.write( "That happens in the following cases:
\n" ); document.write( "(i) x>=0 and x-7>=0
\n" ); document.write( "(ii) x<=0 and x-7<=0
\n" ); document.write( "The zeros of x(x-7) are 0 and 7
\n" ); document.write( "the conditions (i) is valid when x>=7
\n" ); document.write( "the condition (ii) is valid if x<=0
\n" ); document.write( "--------------0------7---------------
\n" ); document.write( " + ~~~~~~~~~~~ - ~~~~~~~~~~ +
\n" ); document.write( "So the intervals for sqr[x(x-7)] to be a real number are (-∞ ,0] and [7,+∞) \n" ); document.write( "

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