Question

Inversa de f(x) = e2x-1

Answer 1

$\text y = \text e^{(2\text x-1)} \\\\ \underline{\text{calculando a inversa. Trocando x por y e isolando o y}}: \\\\ \text x = \text e^{(2\text y-1)} \\\\ \underline{\text{aplicando ln dos dois lados}}: \\\\ \text{ln(x)}=\text{ln}\ \text e^{(2\text y-1)} \\\\ \text{ln(x)} = (2\text y-1).\text{ln e} \\\\ \underline{\text{portanto temos a seguinte inversa }}:\\\\ \huge\boxed{\text y = \frac{\text{ln(x)}+1}{2}} \checkmark$