Question

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

Answer 1

`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`