Question

f:(0.∞)→(0,∞)

f(x)=log₃x+x

Se cere inversa

Answer 1

$f:(0,+\infty)\to (0,+\infty)\\\\ f(x) = \log_{3}x + x$

x = log₃y+y

x = log₃y+ log₃(3ʸ)

x = log₃(y·3ʸ)

3ˣ = y·3ʸ

$y = \dfrac{W(3^x\ln 3)}{\ln 3}\\ \\ \Rightarrow f^{-1}(x) = \dfrac{W(3^x\ln 3)}{\ln 3}$