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How do you find the domain and range of # f(x)=2/(3x-1)#?

Answer 1

Savannah Anderson

The domain is #x in (-oo, 1/3) uu(1/3,+oo)#. The range is #y in (-oo,0) uu(0,+oo)#

The denominator must be #!=0#

Consequently,

#3x-1!=0#

#=>#, #x!=1/3#

The domain is #x in (-oo, 1/3) uu(1/3,+oo)#

To determine the range, follow these steps:

Let #y=2/(3x-1)#

#<=>#, #y(3x-1)=2#

#<=>#, #3yx-y=2#

#<=>#, #3yx=2+y#

#<=>#, #x=(2+y)/(3y)#

The denominator must be #!=0#

#3y!=0#

#=>#, #y!=0#

The range is #y in (-oo,0) uu(0,+oo)#

plot{2/(3x-1) [-12.66, 12.65, -6.33, 6.33]}

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Answer 2

Eva Adamson

Domain: (x \neq \frac{1}{3})
Range: All real numbers except 0.

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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.