# How do you find the domain and range of #(x-2)/(x^2+3x-10)#?

##### 2 Answers

The domain is

#### Explanation:

The denominator is

Therefore,

As the denominator

So,

The domain is

To calculate the range, proceed as follows

Let

So,

Therefore,

The range is

graph{1/(x+5) [-10, 10, -5, 5]}

#### Explanation:

#"let "y=(x-2)/(x^2+3x-10)#

#"factorise numerator/denominator and simplify"#

#y=cancel((x-2))/((x+5)cancel((x-2)))=1/(x+5)#

#"the denominator cannot equal zero as this would make"#

#"y undefined. Equating the denominator to zero and"#

#"solving gives the value that x cannot be"#

#"solve "x+5=0rArrx=-5larrcolor(red)"excluded value"#

#rArr"domain is "x inRR,x!=-5#

#"to find the range rearrange making x the subject"#

#y(x+5)=1larrcolor(blue)"cross-multiply"#

#rArrxy+5y=1#

#rArrxy=1-5y#

#rArrx=(1-5y)/y#

#"the denominator cannot equal zero"#

#rArr"range is "y inRR,y!=0#