Question

f:[2,+∞)->R , f(x)=ln(1+√(x-2))

Aflati m ∈ R astfel incat ecuatia f(x)=m are o singura solutie pe (3,+∞)

Multumesc anticipat ≅≅≅

Answer 1

Răspuns:

Explicație pas cu pas:

$\displaystyle f'(x)=\dfrac{1}{2(1+\sqrt{x-2})\sqrt{x-2}}>0~\forall x\in (2,\infty),\texttt{Prin urmare functia }\\\texttt{este strict crescatoare, deci si injectiva}.\\ \lim_{x\to\infty} f(x)=\infty \text{ si }f(3)=\ln 2\\\texttt{Asadar }m\in(\ln 2,\infty)$