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What is the domain and range of f(x)?  `f(x) = (2x+3)/(x-1)`  f(x) = (2x+3)/(x-1)

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qpqpqpabc | eNotes Newbie

Posted September 30, 2013 at 12:24 PM via web

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What is the domain and range of f(x)?

 `f(x) = (2x+3)/(x-1)` 

f(x) = (2x+3)/(x-1)

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durbanville | High School Teacher | (Level 1) Educator Emeritus

Posted September 30, 2013 at 12:57 PM (Answer #1)

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The domain is the set of values of x (the input values) allowing the function to work properly. In this case  `f(x) = (2x+3)/(x-1)`

x cannot be 1 `x!=1`  ( as this would render the denominator as zero which is undefined.)

`therefore x:{x in RR; x!=1}`

The range is the set of y values (output) that works in the given function. in this case there are no restrictions placed on y and 

`therefore y:{yinRR}`

Ans: 

Domain `{x in RR, x!=1}`

Range`{y in RR}`

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