Q. 55.0( 1 Vote )

Let f : R R : f(x) = x2.

Determine (i) range (f) (ii) {x : f(x) = 4}

Answer :

Given: f(x) = x2


The graph for the given function is



(i) Range(f):


For finding the range of the given function, let y = f(x)


Therefore,


y = x2


x = √y


The value of y ≥ 0.


Hence, Range(f) is [0, ∞).


(ii) Let y = f(x) =


Given y = 4.


Therefore, =4


x = 2 or x = -2


The set of values for which y = 4 is x = {2,-2}.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Trigonometric Functions - 05Trigonometric Functions - 05Trigonometric Functions - 0568 mins
Trigonometric Functions - 01Trigonometric Functions - 01Trigonometric Functions - 0152 mins
Conditional IdentitiesConditional IdentitiesConditional Identities31 mins
Trigonometric Functions - 06Trigonometric Functions - 06Trigonometric Functions - 0658 mins
Let's Play the Game of InequalitiesLet's Play the Game of InequalitiesLet's Play the Game of Inequalities52 mins
Trigonometric Functions - 03Trigonometric Functions - 03Trigonometric Functions - 0366 mins
Cell - The unit of Life - 02Cell - The unit of Life - 02Cell - The unit of Life - 0268 mins
Trigonometric SeriesTrigonometric SeriesTrigonometric Series45 mins
Trigonometric Functions - 08Trigonometric Functions - 08Trigonometric Functions - 0865 mins
Trigonometric Functions - 07Trigonometric Functions - 07Trigonometric Functions - 0760 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses