For the given function $f(x)$, find its inverse.
-$f(x)=\ln (x+3)+8$
A) $\mathrm{f}^{-1}(\mathrm{x})=\mathrm{e}^{\mathrm{x}-8}-3$
B) $\mathrm{f}^{-1}(\mathrm{x})=\mathrm{e}^{\mathrm{x}-3}-8$
C) $f^{-1}(x)=e^{x-3}+8$
D) $\mathrm{f}^{-1}(\mathrm{x})=\mathrm{e}^{\mathrm{x}-8}+3$

Question

Quizplus · Accepted Answer

To find the inverse of $f(x)=\ln(x+3)+8$, you swap $x$ and $y$ and solve for $y$. So, $x=\ln(y+3)+8$. Isolate the logarithm: $x-8=\ln(y+3)$. Then, exponentiate both sides to get rid of the logarithm: $e^{x-8}=y+3$. Finally, solve for $y$: $y=e^{x-8}-3$, which corresponds to $f^{-1}(x)=e^{x-8}-3$.

For the Given Function f(x)f(x)f(x) , Find Its Inverse f(x)=ln⁡(x+3)+8f(x)=\ln (x+3)+8f(x)=ln(x+3)+8 A) f−1(x)=ex−8−3\mathrm{f}^{-1}(\mathrm{x})=\mathrm{e}^{\mathrm{x}-8}-3f−1(x)=ex−8−3

For the Given Function $f(x)$ , Find Its Inverse $f(x)=\ln (x+3)+8$ A) $\mathrm{f}^{-1}(\mathrm{x})=\mathrm{e}^{\mathrm{x}-8}-3$