SOLUTION: 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
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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
Found 3 solutions by MathLover1, greenestamps, ikleyn:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
The domain of a radical function is any x value for which the radicand (the value under the radical sign) is not negative.
will be all values of that make
factor
solutions
if
or
if
so domain is
{ element : or }
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
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.
The given function is
The domain of the function is those values of x that make greater than or equal to 0. To determine those values, factor the quadratic:
The quadratic is equal to zero when either of those factors is zero.
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.
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.
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.
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
Answer by ikleyn(52790) (Show Source): You can put this solution on YOUR website!
.
I came to fix the answer given by @greenestamps.
The correct ANSWER is THIS : the domain is the set {x <= -2.5} OR {x >= 4}.
In this problem, endpoints of semi-infinite intervals are included in the domain
(@greenestamps excluded them in his answer).
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