How do you find domain and range for # f(x) = sqrt(7x + 2)#?

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Answer 1 · 2018-06-28T16:12:57

The domain is #x in [-2/7, +oo)#. The range is #y in [0,+oo)#

Let #y=sqrt(7x+2)#

What's under the square root sign is #>=0#

Therefore,

#7x+2>=0#

#=>#, #x>=-2/7#

The domain is #x in [-2/7, +oo)#

When,

#x=-2/7#, #=>#, #y=0#

And

#lim_(x->+oo)sqrt(7x+2)=+oo#

Therefore,

The range is #y in [0,+oo)#

graph{sqrt(7x+2) [-7.06, 21.42, -7.46, 6.78]}