Determining If a Function is InvertibleĪs we had discussed above the conditions for the function to be invertible, the same conditions we will check to determine that the function is invertible or not. Since function f(x) is both One to One and Onto, function f(x) is Invertible. To show that the function is invertible or not we have to prove that the function is both One to One and Onto i.e, Bijective Show that f is invertible, where R + is the set of all non-negative real numbers.
Since we proved the function both One to One and Onto, the function is Invertible.Įxample 3: Consider f: R + -> given by f(x) = x 2 + 4.
Let’s see some examples to understand the condition properly.Įxample 1: Let A : R –. When we prove that the given function is both One to One and Onto then we can say that the given function is invertible. We can say the function is Onto when the Range of the function should be equal to the codomain. We can say the function is One to One when every element of the domain has a single image with codomain after mapping. Conditions for the Function to Be InvertibleĬondition: To prove the function to be invertible, we need to prove that, the function is both One to One and Onto, i.e, Bijective. So, the function f(x) is an invertible function and in this way, we can plot the graph for an inverse function and check the invertibility. Class 12 NCERT Solutions- Mathematics Part I - Application of Derivatives - Exercise 6.2| Set 2Īfter drawing the straight line y = x, we observe that the straight line intersects the line of both of the functions symmetrically.Difference between write() and writelines() function in Python.Second Order Derivatives in Continuity and Differentiability | Class 12 Maths.How to Connect Python with SQL Database?.Properties of Matrix Addition and Scalar Multiplication | Class 12 Maths.Torque on an Electric Dipole in Uniform Electric Field.Graphs of Inverse Trigonometric Functions - Trigonometry | Class 12 Maths.Matrices and its Types | Class 12 Maths.Graphical Solution of Linear Programming Problems.Shortest Distance Between Two Lines in 3D Space | Class 12 Maths.Class 12 NCERT Solutions - Mathematics Part I - Chapter 2 Inverse Trigonometric Functions - Exercise 2.1.ISRO CS Syllabus for Scientist/Engineer Exam.ISRO CS Original Papers and Official Keys.GATE CS Original Papers and Official Keys.
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