Answer :

Given:


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.


Graph:



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