How do you find the domain and range of f(x)=6/(9-5x)?

1 Answer
Jim G.
Oct 30, 2017

x inRR,x!=9/5,y inRR,y!=0

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 value that x cannot be.

"solve "9-5x=0rArrx=9/5larrcolor(red)"excluded value"

rArr"domain is "x inRR,x!=9/5

"let " y=6/(9-5x)

"rearrange making x the subject"

rArry(9-5x)=6larrcolor(blue)"cross-multiplying"

rArr9y-5xy=6

rArr-5xy=6-9y

rArrx=(6-9y)/(-5y)

"the denominator cannot equal zero"

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

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