Find the domain and the range of the cube root function,

f: R R: f(x) = x1/3 for all x ϵ R. Also, draw its graph.


f(x) = x1/3 x є R

To Find: Domain and range of the given function.

Here, f(x) = x1/3

The domain of the above function would be,

Domain(f) = (-∞, ∞) {x | x є R}

Because all real numbers have a cube root. There is no value of x which makes the function undefined.

Now, to find the range

Consider f(x) = y

Then, y = x1/3

y3 = x

Since f(x) is continuous, it follows that

Range(f) = (-∞, ∞) {y | y є R}

Because for every value of y there would be a cube of that value.