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

1 Answer
Binayaka C.
Jun 29, 2017

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]

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