## Calculus: Early Transcendentals 8th Edition

a) $x\gt\ln3$ b)$f^{-1}(x)=\ln(e^x+3)$ Domain: all real x
a) $e^x-3\gt0$ $e^x\gt3$ $x\gt\ln3$ b) $y=f(x)=\ln(e^x-3)$ $e^x-3=e^y$ $e^x=e^y+3$ $x=\ln(e^y+3)$ $y\rightleftharpoons x$: $f^{-1}(x)=y=\ln(e^x+3)$ $\because e^x+3\gt0$ for all real x, the domain is all real x