# 4. State the domain of the function f, defined by f(x) = (x-2)/(x2 − 3x)√6 − x.

4. State the domain of the function f, defined by f(x) = (x-2)/(x2 − 3x)√6 − x.

## the answer is

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xxxx xx xxxxxxxxx x x^2(x-3)

xxxxxxxx x: x xx all real xxxxxx xxxxx xxxx 0 xxx 3}

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## (-infinity,6]-{0,3}

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xxx the xxxxx xxxxxxxx to xx defined xxxx should not xx imaginary xx xx xxxxxx xxx be infinity(i.e, xxx denominator xxxxxx not xx xxxxxx

To solve xxxx problem xxxx xxxxx find xxx xxxxxx at which its is xxx defined as there xxx xxxx a xxx points xx which xx xxxx not xx xxxxxxxx

xxxxxxxxx

xxxxxxx for f(x) to be undefined that xx

xxxxx xxxxxxxx xx

x=0 xxx xxxx

also 6-x<0 for f(x) to be undefined as 6-x is under the square root and the square root of a negative no. is imaginary.

therefore xxx xxx xxxx xx xxx defined.i.e., x xxxxxxx to (6,infinity).

xxxxxxxxx xxxxxx xx xxxx xxxxxxx minus these numbers.

xxxxxxxxx

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

therefore answer xx

xxxxxxxxxxxxxxxxxxxx

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