RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 3. Functions

Subject: Maths - Class 11th

Q. No. 4 of Exercise 3D

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4

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.


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:



Chapter Exercises

More Exercise Questions

2

Consider the function f: R R, defined by

Write its domain and range. Also, draw the graph of f(x).