How do you find the domain and range for #g(x)=sqrt( x-1)#?

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Answer 1 · 2017-12-17T07:18:43

The domain is #x in [1, +oo)#. The range is #g(x) in [0, +oo)#

What's under the #sqrt# sign is #>=0#

Therefore,

#x-1>=0#

#x>=1#

The domain is

#x in [1, +oo)#

When #x=1#, #=>#, #y=0#

And

#lim_(x->+oo)g(x)=lim_(x->+oo)sqrt(x-1)=+oo#

The range is #g(x) in [0, +oo)#

graph{sqrt(x-1) [-10, 10, -5, 5]}