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

1 Answer
Jun 29, 2017

Answer:

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]