1 Real Mathematical Analysis Please provide complete and cor

1. Real (Mathematical) Analysis. Please provide complete and correct solution done on computer or by hand with mathematical proof/explanation to all questions. Please, emphasis on complete and correct solution. The answers will be verified. This is all the information provided. Thank you very much.

1. Consider the function f R given by T12 2 (a) At which points can we apply the inverse function theorem? (b) et (T1, a2) be one of the points you found in (a) We know from the Inverse Function Theorem that in some neighborhood of a, f has an inverse. What is the derivative of that inverse at a

Solution

a) we can apply the inverse functions on both points as they gives th values of the function as continuous

the proof is in the uploaded pic