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Domain | y = sqrt(36 - x^2)/sqrt(x^2 - 4 (x + 3)^2)

I got {-6,-2}
There's another answer in the textbook, what did i miss?

1 Answer

1 vote

Explanation:

I think you may have forgotten you cannot have a sqrt of a negative number ....

The domain is the set of x values the function can have

all x EXCEPT values that cause

the denominator to = 0 OR be a sqrt 0f a negative number OR cause numerator to be sqrt of a negative

So for the numerator portion: x > 6 not allowed....

For the denominator:

sqrt ( x^2-4(x+3)^2 ) cannot equal 0

and 4 (x+3)^2 cannot = x^2

4x^2 +24x + 36 cannot = x^2

3x^2 + 24x + 36 cannot = 0

3 (x^2 + 8x+12) cannot = 0

x^2 + 8x + 12 cannot = 0

(x+2)(x+6) cannot = 0

x cannot = -2 or -6

then x^2-4(x+3)^2 <0 not allowed ( it would be sqrt of a negative)

x^2 - 4x^2 -24x-36 <0 not allowed

-3x^2 -24x -36 <0 not allowed

-3 ( x^2 +8x+12) <0

(x+6)(x+2) < 0 not allowed <=====this is a dome shaped parabola (see attached image)

so greater than -2 or less than -6 not allowed

Domain is then -2>x>-6 ( or re-written as -6<x<-2 )

Is what I find -6 and -2 cannot be included....the denom would be 0 (as found above) I do not know where -3 comes from ....

I submitted this to Wolframalpha and this is the answer it found too...so I think your textbook is in error.....

Domain | y = sqrt(36 - x^2)/sqrt(x^2 - 4 (x + 3)^2) I got {-6,-2} There's another-example-1
User Mordaroso
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