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The exercise you've uploaded asks to determine \( f(I) \), verify that \( f \) is a bijection, and then specify \( f^{-1} \) for given functions \( f(x) \) and intervals \( I \).

Here’s a breakdown of the exercise:

### For each of the following cases, determine \( f(I) \) and verify that \( f \) defines a bijection from \( I \) to \( f(I) \). Then, specify \( f^{-1} \), the inverse of \( f \).

#### Case 1:
\( f(x) = x^2 - 4x + 3 \)  
\( I = ]-\infty, 2] \)

#### Case 2:
\( f(x) = \frac{1}{x} \)  
\( I = ]0, 1] \)

Would you like me to solve both cases in detail? Feel free to ask any clarifications!

Dans chacun des cas suivants, déterminer f(I), puis vérifier que f réalise une bijection de I sur J = f(I), puis préciser f^{-1} pour f(x) = x^2 - 4x + 3, I = ]-∞, 2], et f(x) = 1/x, I = ]0, 1].

This exercise focuses on determining the image of a function f over a given interval I, verifying that f is a bijection, and finding its inverse f^{-1}. Explore quadratic and rational functions for I = ]-∞, 2] and I = ]0, 1].

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