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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