Question #fcfb5

1 Answer
  1. (-infinity, #<-3#), U #(>3#, infinity)
  2. (-infinity, #<2#), U #(>2#, infinity)
  3. (-infinity, #<=0)#, U #(>0#, infinity)

Explanation:

  1. #f(x)#=#(sqrt(x+1))/(x^2-9)#
    Here, considering denominator, #(x^2-9) #
    which becomes zero when #x=+-3# leads us to the value of the function to take infinity.
    Hence the domain happens to be,
    Set of all real numbers except -3 and +3
    (-infinity, #<-3#), U #(>3#, infinity)

2.#f(x)#=#x^4log(x-2) #
Here, consider the term #x-2#, which is zero at x=2, when #log(x-2)# is - infinity
Hence, the domain happens to be
Set of all real numbers except 2
(-infinity, #<2#), U #(>2#, infinity)

3 In this function the function is not unique at x = 0.
Hence, the domain happens to be set of all real numbers except 0
(-infinity, #<=0)#, U #(>0#, infinity)