What is the domain of #f(x)= (8x)/((x-1)(x-2))#?

Answer 1

It is all the real numbers except those that nullify the denominator in our case x=1 and x=2. So the domain is #R-{1,2}#

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Answer 2

The domain is all the real numbers except x can not be 1 or 2.

#f(x) = (8x)/[(x - 1)(x - 2)]#

A function's domain is its set of points where it is defined. Since we are unable to divide by zero, the roots of the denominators represent the points where the function is not defined, so we can quickly identify the point or points where it is undefined and remove them from the domain:

#(x - 1)(x - 2) = 0# => using the The Zero Product Property which states that if ab = 0, then either a = 0 or b = 0 (or both), we get:
#x - 1 = 0 => x = 1# #x - 2 = 0 => x = 2#
Hence the domain is all the real numbers except 1 or 2. in interval notation: #(-oo , 1) uuu(1 , 2)uuu (2 , oo)#
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Answer 3

The domain of ( f(x) = \frac{8x}{(x-1)(x-2)} ) is all real numbers except ( x = 1 ) and ( x = 2 ), since these values would make the denominator zero, which is undefined.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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