SOLUTION: Please help: Find the domain for f(x)= {{{ (sqrt((x+3)(7-x))+ sqrt((x-1)(9-x))) / sqrt((x-2)(x-5)) }}}

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Question 690009: Please help: Find the domain for f(x)=
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
You can't divide by zero, so (x-2)(x-5) can't be zero.

(x-2)(x-5) must be positive since you cannot take the square root of a negative number.

So (x-2)(x-5) > 0


(x-2)(x-5) has the zeros x = 2 or x = 5. (x-2)(x-5) is positive when either x < 2 or x > 5. You can see this you plug in values such as x = 1 or x = 6.

(x-2)(x-5) is negative when 2 < x < 5. You can see this you plug in values such as x = 3 or x = 4.

So the domain in interval notation is