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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