What is the range of the function #f(x)=2/(x+3) -4#?

1 Answer
Apr 30, 2017

Answer:

#y inRR,y!=-4#

Explanation:

#"Rearrange f(x) to make x the subject"#

#y=f(x)=2/(x+3)-(4(x+3))/(x+3)#

#rArry=(2-4x-12)/(x+3)=(-4x-10)/(x+3)#

#color(blue)"cross-multiply"#

#rArryx+3y=-4x-10#

#rArryx+4x=-10-3y#

#rArrx(y+4)=-10-3y#

#rArrx=(-10-3y)/(y+4)#

The denominator cannot be zero as this would make the function #color(blue)"undefined".#Equating the denominator to zero and solving gives the value that y cannot be.

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

#"range " y inRR,y!=-4#