Question

For the function \[f(x)=\sqrt[3]{(x-2)}+3\] would it be undefined at all real number or just 2 or am I wrong?

Answer 1

You're wrong.

Answer 2

YOu can take the cubed root of zero and negative numbers so it should be defined everywhere

Answer 3

It's defined for all real numbers. Here is the graph: https://www.desmos.com/calculator/opzjry2i4c

Answer 4

but i need to figure out where it would be Undefined. so it would be undefined at all real numbers?

Answer 5

finding the values for which the function is undefined is same as finding the values of x not in the domain of f(x)

Answer 6

so, could you first find the domain of f(x) ?
hint : the quantity under \(\large \sqrt[3]{...}\)
must be non--negative

Answer 7

The quantity under the cubed root does not have to be non negitve. \[\sqrt[3]{-1}=-1\]

Answer 8

That function is defined everywhere.

Answer 9

i am sorry, thats correct.
the function is defined everywhere.