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June 11th, 2017, 01:25 PM   #1
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finding domain of square root function

State the domain of the following function using interval notation.

sqrt( -x^2 +10x -21)

I got this answer (-infinity, -5-sqrt(46)] U [sqrt(46) -5, infinity) but it can't even be inputted in the answer part

the answer part is as follows,(________,________) so I am not sure what to do.
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June 11th, 2017, 01:55 PM   #2
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The zeros of the function are $\displaystyle \sqrt{3}\ and\ \sqrt{7}$. The domain is that interval, since function is imaginary outside.
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June 11th, 2017, 01:56 PM   #3
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Quote:
Originally Posted by mathishard23 View Post
State the domain of the following function using interval notation.

sqrt( -x^2 +10x -21)

I got this answer (-infinity, -5-sqrt(46)] U [sqrt(46) -5, infinity) but it can't even be inputted in the answer part

the answer part is as follows,(________,________) so I am not sure what to do.
$-x^2 + 10x - 21 \geq 0$

$x^2 - 10x + 21 \leq 0$

$(x-7)(x-3) \leq 0$

$(x-7)\leq 0 \wedge (x-3)\geq 0 \bigvee (x-7)\geq 0 \wedge (x-3)\leq 0$

$x\leq 7 \wedge x\geq 3 \bigvee x \geq 7 \wedge x \leq 3$

the right hand condition is the empty set leaving

$x \in [3, 7]$
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June 11th, 2017, 02:37 PM   #4
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That was correct thank you. I am still wondering though how you ignored the square root. the roots are 3 and 7 but what about thw square root do you just ignore it or...
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June 11th, 2017, 02:53 PM   #5
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Originally Posted by mathishard23 View Post
That was correct thank you. I am still wondering though how you ignored the square root. the roots are 3 and 7 but what about thw square root do you just ignore it or...
You are concerned about the expression under the radical ... one may take the square root of zero or positive values only, hence ...

$-x^2+10x-21 \ge 0$

... as written by romsek.

The values of x in the interval [3,7] satisfy this requirement ... all other values of x make the quadratic expression negative.
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June 11th, 2017, 02:59 PM   #6
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You are concerned about the expression under the radical ... one may take the square root of zero or positive values only, hence ...

$-x^2+10x-21 \ge 0$

... as written by romsek.

The values of x in the interval [3,7] satisfy this requirement ... all other values of x make the quadratic expression negative.
oh ok i get it thats y he made it an inequality type thing thanks
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