# What is the domain and range of #f (x) = (x^2-2)/(x^2-4)#?

##### 2 Answers

Domain and range of this function

#### Explanation:

Domain:

Range:

#### Explanation:

The denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the values that x cannot be.

#"solve " x^2-4=0rArrx^2=4#

#rArrx=+-2larrcolor(red)" excluded values"#

#rArr"domain is " x inRR,x!=+-2# To find the value that y cannot be find

#lim_(xto+-oo)f(x)# divide terms on numerator/denominator by the highest power of x, that is

#x^2#

#f(x)=(x^2/x^2-2/x^2)/(x^2/x^2-4/x^2)=(1-2/x^2)/(1-4/x^2)# as

#xto+-oo,f(x)to(1-0)/(1-0)#

#rArryto1larrcolor(red)" excluded value"#

#rArr"range is " y inRR,y!=1# The graph of f(x) illustrates this.

graph{(x^2-2)/(x^2-4) [-10, 10, -5, 5]}