# 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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f(x) xx xxxxxxxxx x x^2(x-3)

xxxxxxxx x: x xx all xxxx xxxxxx xxxxx than 0 and 3}

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

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for the xxxxx xxxxxxxx to be xxxxxxx f(x) should xxx xx xxxxxxxxx xx it should not be xxxxxxxxxxxxx xxx xxxxxxxxxxx xxxxxx not xx zero).

xx xxxxx xxxx xxxxxxx xxxx first find the points at xxxxx xxx is xxx defined xx there xxx only x xxx xxxxxx at which xx will xxx xx defined.

xxxxxxxxx

xxxxxxx xxx f(x) to xx xxxxxxxxx that is

xxxxx xxxxxxxx or

xxx xxx x=3.

also xxx<x xxx f(x) to be undefined as xxx is xxxxx xxx xxxxxx root xxx xxx xxxxxx xxxx xx a xxxxxxxx no. is xxxxxxxxxx

therefore for x>6 xxxx xx xxx defined.i.e., x belongs to (6,infinity).

xxxxxxxxx xxxxxx is real xxxxxxx minus these xxxxxxxx

therefore

(-infinity,infinity)-(6,infinity)-{0,3}

therefore answer is

xxxxxxxxxxxxxxxxxxxx

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