What is the domain and range of #h(x)=-sqrt(x^2-16) -3#?

1 Answer
Shwetank Mauria
Dec 29, 2017

Domain for #h(x)# is #x<=-4# and #x>=4#. Range for #h(x)# is #(-oo,-3)#.

Explanation:

It is apparent that #x^2-16>0#, hence we must #x<=-4# or #x>=4# and that is the domain for #h(x)#.

Further the least value for #sqrt(x^2-16)# is #0# and it can up to #oo#.

Hence range for #h(x)=-sqrt(x^2-16)-3# is from a minimum of #-oo# to maximum of #-3# i.e. #(-oo,-3)#.

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