What is the domain and range of f(x) = 7/(x+3)?

1 Answer
Jim G.
Jun 20, 2018

x inRR,x!=-3,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 "x+3=0rArrx=-3larrcolor(red)"excluded value"

"domain is "x inRR,x!=-3

(-oo,-3)uu(-3,oo)larrcolor(blue)"in interval notation"

"let "y=7/(x+3)

"for range, rearrange making x the subject"

y(x+3)=7

xy+3y=7

xy=7-3y

x=(7-3y)/ytoy!=0

"range is "y inRR,y!=0

(-oo,0)uu(0,oo)
graph{7/(x+3) [-10, 10, -5, 5]}

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