Question

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

Answer 1

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]}