Question

se f(x)= logx e a.b=1, então f(a)+f(b) é igual a

Answer 1

$f(x)=\mathrm{\ell og\,}x$

Se $a\cdot b=1,$ então

$b=\dfrac{1}{a}\;\;\Rightarrow\;\;b=a^{-1}$


Portanto,

$f(a)+f(b)\\ \\ =\mathrm{\ell og\,}a+\mathrm{\ell og\,}b\\ \\ =\mathrm{\ell og\,}a+\mathrm{\ell og\,}(a^{-1})\\ \\ =\mathrm{\ell og\,}a+(-1)\cdot \mathrm{\ell og\,}a\\ \\ =\mathrm{\ell og\,}a-\mathrm{\ell og\,}a\\ \\ =0$