Question

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.

Answer 1

Question:

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.

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Step-by-step explanation:

Given:

• f(x) = x1/3∀ x є R

To Find:

• Domain and range of the given function.

f(x) = x1/3

Domain(f) = (-∞, ∞) {x | x є R}

There is no value of x which makes the

function undefined.

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Consider f(x) = y

Then, y = x1/3y

3 = x

Since f(x) is continuous, it follows that

Range(f) = (-∞, ∞) {y | y є R}

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