How do you find the domain and range of #root5(-4-7x)#?

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Answer 1 · 2018-06-21T14:49:32

See below

This is an odd number root, so negative values for the radicand are allowed. Therefore domain is:

#{x in RR }#

or

#(-oo,oo)#

For the range we observe what happens as x goes to #+-oo#

as: #x->oo# , #color(white)(8888)-4-7x->-oo#

as: #x->-oo# , #color(white)(8888)-4-7x->oo#

Therefore the range is:

#{f(x) in RR}#

or

#(-oo,oo)#

The graph of #f(x)=root(5)(-4-7x) # confirms this:

graph{y=root(5)(-4-7x) [-10, 10, -5, 5]}