How do you find the domain and range of #root4(-4-7x)#?

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Answer 1 · 2018-01-17T13:33:22

The domain is #x in (-oo, -4/7]#. The range is #y in [0,+oo)#

Let #y=(-4-7x)^(1/4) #

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

Therefore,

#-4-7x>=0#

#7x<=-4#

#x<=-4/7#

The domain is #x in (-oo, -4/7]#

When #x=-4/7#, #=>#, #y=0#

When #x=-oo#, #=>#, #y=+oo#

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

graph{(-4-7x)^(1/4) [-12.66, 12.65, -6.33, 6.33]}