How do you find the domain and range of #f(x)=5/(x-3)#?

Answer 1

The domain is #x in (-oo,3)uu(3,+oo)#. The range is #y in (-oo,0)uu(0,+oo)#

The denominator must be #!=0#

Consequently,

#x-3!=#
#=>#, #x!=3#
The domain is #x in (-oo,3)uu(3,+oo)#

To determine the range, follow these steps:

Let #y=5/(x-3)#
#y(x-3)=5#
#yx-3y=5#
#yx=5+3y#
#x=(5+3y)/(y)#
The denominator is #!=0#
#y!=0#
The range is #y in (-oo,0)uu(0,+oo)#

diagram{5/(x-3) [-18.02, 18.02, -9.01, 9.02]}

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Answer 2

To find the domain of the function f(x) = 5/(x - 3), we need to determine all the values of x for which the function is defined. Since the function involves division by (x - 3), x cannot equal 3 because division by zero is undefined. Therefore, the domain of the function is all real numbers except x = 3.

To find the range of the function, we consider the behavior of the function as x approaches positive infinity and negative infinity. As x approaches positive infinity, the denominator (x - 3) approaches positive infinity, causing the entire fraction to approach zero. As x approaches negative infinity, the denominator (x - 3) approaches negative infinity, causing the entire fraction to approach zero. Therefore, the range of the function is all real numbers except zero.

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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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