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

↳Redirected from "Suppose that I don't have a formula for #g(x)# but I know that #g(1) = 3# and #g'(x) = sqrt(x^2+15)# for all x. How do I use a linear approximation to estimate #g(0.9)# and #g(1.1)#?"
1 Answer
Somebody N.
Jun 21, 2018

See below

Explanation:

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]}

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