How do you find the domain and range of #y=(3x-2)/(4x+1)#?

1 Answer
Jim G.
Jan 16, 2018

#x inRR,x!=-1/4#
#y inRR,y!=3/4#

Explanation:

The denominator of y cannot be zero as this would make y undefined. Equating the denominator to zero and solving gives the value that x cannot be.

#"solve "4x+1=0rArrx=-1/4larrcolor(red)"excluded value"#

#rArr"domain is "x inRR,x!=-1/4#

#"for the range rearrange making x the subject"#

#rArry(4x+1)=3x-2#

#rArr4xy+y=3x-2#

#rArr4xy-3x=-2-y#

#rArrx(4y-3)=-2-y#

#rArrx=(-2-y)/(4y-3)#

#"solve "4y-3=0rArry=3/4larrcolor(red)"excluded value"#

#"range is "y inRR,y!=3/4#

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