What is the domain and range of #f(x) =x^2/ (x^2-6)#?

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Answer 1 · 2018-04-15T23:51:54

Domain: #x≠sqrt6#

Range: #yinRR#

First, it is important to understand the distinction between domain and range.

Domain:
All possible #x#-values for the expression

Range:
All possible #y#-values for the expression

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Finding the Domain:

On the numerator, the #x#-value can be any real number

The denominator however, #≠ 0# since that would make the function undefined.

So, to find the number that #x# cannot equal in the function, we must write:

Denominator#=0#

#x^2-6=0#

#x^2=6#

#sqrt(x^2)=sqrt6#

#therefore x=sqrt6# when the function is undefined

This means that the domain is: #x≠sqrt6#

Finding the Range:

#f(x)# just means that #x# is the input of the function.

The actual result of the equation is #y#, do the function can be rewritten as:

#y=x^2/(x^2-6)#

Now there is a #y#-value to work with. Since there are no limitations on the value of #y# in the equation, it can be any real number.

This means that the range is: #yinRR#

or

#y# can be any real number