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

1 Answer
Amal R.
Apr 15, 2018

Domain: x≠sqrt6

Range: yinRR

Explanation:

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

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