
Whether the below function is an increasing function and find out if the inverse of the function exists. If the inverse exists, find out the inverse of the function.
To find if the inverse of the function exists:
For the interval ,
Let us assume that if
Then,
Thus, the inverse of the function exists.
For the interval ,
Let us assume that if
Then,
Thus, the inverse of the function exists.
Hence, we get that the inverse of the function exists.
Inverse of the function:
For the interval ,
Replacing with , we get
On switching and , we get
Solving for , we get
Replacing with , we get
For the interval ,
Replacing with , we get
On switching and , we get
Solving for , we get
Replacing with , we get
Thus, Inverse of function is

Want to see the full answer?
Check out a sample textbook solution
Chapter 1 Solutions
Loose-leaf Version for Calculus: Early Transcendentals Combo 3e & WebAssign for Calculus: Early Transcendentals 3e (Life of Edition)
- Solve by DrWz WI P L B dy Sind Ⓡ de max ⑦Ymax dx Solve by Dr ③Yat 0.75m from A w=6KN/M L=2 W2=9 kN/m P= 10 KN Solve By Drarrow_forwardHow to find the radius of convergence for the series in the image below? I'm stuck on how to isolate the x in the interval of convergence.arrow_forwardDetermine the exact signed area between the curve g(x): x-axis on the interval [0,1]. = tan2/5 secx dx andarrow_forward
- A factorization A = PDP 1 is not unique. For A= 7 2 -4 1 1 1 5 0 2 1 one factorization is P = D= and P-1 30 = Use this information with D₁ = to find a matrix P₁ such that - -1 -2 0 3 1 - - 1 05 A-P,D,P P1 (Type an integer or simplified fraction for each matrix element.)arrow_forwardMatrix A is factored in the form PDP 1. Use the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace. 30 -1 - 1 0 -1 400 0 0 1 A= 3 4 3 0 1 3 040 3 1 3 0 0 4 1 0 0 003 -1 0 -1 Select the correct choice below and fill in the answer boxes to complete your choice. (Use a comma to separate vectors as needed.) A basis for the corresponding eigenspace is { A. There is one distinct eigenvalue, λ = B. In ascending order, the two distinct eigenvalues are λ₁ ... = and 2 = Bases for the corresponding eigenspaces are { and ( ), respectively. C. In ascending order, the three distinct eigenvalues are λ₁ = = 12/2 = and 3 = Bases for the corresponding eigenspaces are {}, }, and { respectively.arrow_forwardN Page 0.6. 0.4. 0.2- -0.2- -0.4- -6.6 -5 W 10arrow_forward
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning





