Find the inverse of the function.
-$$f ( x ) = e ^ { 7 x }$$
A) $f ^ { - 1 } ( x ) = 7 \ln x$
B) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 1 } { 7 } \ln \mathrm { x }$
C) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \ln \left( \frac { 1 } { 7 } \mathrm { x } \right)$
D) $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = - 7 \ln \mathrm { x }$

Question

Quizplus · Accepted Answer

To find the inverse of the function $f(x) = e^{7x}$, you swap $x$ and $y$ and solve for $y$. So, $x = e^{7y}$. Taking the natural logarithm of both sides gives $\ln(x) = 7y$, and solving for $y$ gives $y = \frac{1}{7}\ln(x)$, which corresponds to option B.

Find the Inverse of the Function f(x)=e7xf ( x ) = e ^ { 7 x }f(x)=e7x

Find the Inverse of the Function $f ( x ) = e ^ { 7 x }$