document.write( "Question 1196095: What is the domain of the radical function f of x is equal to the square root of the quantity 2 times x squared minus 3 times x minus 20 end quantity \n" ); document.write( "

Algebra.Com's Answer #828794 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "It is POSSIBLE that tutor MathLover1 is using a valid method to solve the problem; however, what she APPEARS to be doing is not valid.

\n" ); document.write( "The given function is

\n" ); document.write( " $\"sqrt%282x%5E2-3x-20%29\"$

\n" ); document.write( "The domain of the function is those values of x that make $\"2x%5E2-3x-20\"$ greater than or equal to 0. To determine those values, factor the quadratic:

\n" ); document.write( " $\"%282x%2B5%29%28x-4%29%3E=0\"$

\n" ); document.write( "The quadratic is equal to zero when either of those factors is zero.

\n" ); document.write( "From there, the other tutor appears to then be solving the problem by finding separately where x-4 is greater than zero and where 2x+5 is greater than zero. That is not a valid method.

\n" ); document.write( "One valid method for determining the domain is to use the two zeroes of the function, at x = -2/5 and x = 4, to divide the set of x values into three intervals and determine in which of those intervals the function value is positive. That will show that the function value is positive for x < -2.5 and for x > 4 and negative for -2.5 < x < 4.

\n" ); document.write( "Another simple valid method is to recognize that the graph of the quadratic is an upward-opening parabola, so it is negative only between x = -2.5 and x = 4.

\n" ); document.write( "Either way, the correct domain is determined: (corrected answer; the endpoints of the intervals are included in the domain): x <= -2.5 or x >= 4

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