How do you find the domain and range of #(x - 2 )/ (x^2- 16)#?

1 Answer
Oct 12, 2017

Answer:

Domain : # x in RR | x != -4, x != 4 # ,in interval notation , #(-oo, -4)uu(-4,4) uu(4,oo)#
Range : # f(x) in RR or (-oo , oo)#

Explanation:

#f(x)= (x-2)/(x^2-16) = (x-2)/((x+4)(x-4))# .

Domain (input #x#) : Denominator should not be zero ,otherwise

#f(x)# will be undefined #:.x+4 != 0 or x != -4 # and

#x-4 != 0 or x != 4 #, so #x# can be any real number except

#x=4 or x= -4#

Domain : # x in RR | x != -4, x != 4 # or

in interval notation , #(-oo, -4)uu(-4,4) uu(4,oo)#

Range : #f(x)# can be any real number

Range : # f(x) in RR or (-oo , oo)#

graph{(x-2)/(x^2-16) [-10, 10, -5, 5]}