What is the domain and range of #3sqrt( x^2 - 9)#?

1 Answer

Answer:

Domain: #x<=-3# or #x>=3# also Domain: #(-oo,-3] uu [3, oo)#
Range: # [0, +oo)#

Explanation:

x can take on values -3 or less up to #-oo#
also x can take on values 3 or higher up to #+oo#

that is why Domain :#x<=-3# or #x>=3#

The lowest possible value is 0 up to #+oo# and that is the range .
That is if we let

#y=3*sqrt(x^2-9)#

when #x=+-3# the value of #y=0# and when #x# approaches a very high value, the value of #y# approaches a very high value also.

So the Range: #[0, +oo)#