Question

What is the domain and range of `f(x)= (2-x)/(x^2+7x+12)`?

Answer 1

Domain: `x in RR` except `x= -3 or x= -4`. In interval notation:`(-oo , -4) uu (-4 , -3) uu (-3,oo)` , Range : Any real number i.e `f(x) in RR`. In interval notation: `(-oo , oo)`

Explanation:

`f(x) = (2-x)/(x^2+7x+12) or f(x)= (2-x)/((x+4)(x+3))`

Domain: Input restriction is denominator should not be `0`

So `(x+4) != 0 or x != -4 and (x+3) != 0 or x != -3`

Domain: `x in RR` except `x= -3 or x= -4`. In interval notation:

`(-oo , -4) uu (-4 , -3) uu (-3,oo)`

Range : Any real number i.e `f(x) in RR`. In interval notation:

`(-oo , oo)`

graph{(2-x)/(x^2+7x+12) [-160, 160, -80, 80]} [Ans]