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#