Réponse :
f(x) = x/(x - 1)
2) soient x , x' ∈ Df tel que x ≠ x'
Tf = (f(x) - f(x'))/(x - x')
f(x) - f(x') = x/(x - 1)] - x'/(x' - 1) = [x(x' - 1) - x'(x - 1)]/(x - 1)(x' - 1)
= (xx' - x - x'x + x')/(x - 1)(x' - 1)
= - (x - x')/(x - 1)(x' - 1)
Tf = - (x - x')/(x - 1)(x' - 1)(x - x') = - 1/(x - 1)(x' - 1)
Explications étape par étape :