The provided solution covers questions about the domain of a logarithmic function, finding its inverse, transformations, and solving inequalities using reflections. Which original question does this s

The equation of $f^{-1}$ is $\boxed{\mathbf{y = 3^{-x}}}$.

From 5.2, $f^{-1}(x) = 3^{-x}$.

To change $3^{-x}$ to $3^x$, we replace $x$ with $-x$. This is a reflection in the y-axis.
To change $3^x$ to $3^x - 5$, we subtract 5 from the function. This is a vertical shift downwards by 5 units.
The transformations are:

• Reflection in the y-axis.
• Vertical shift 5 units downwards.

The function $f(x) = -\log_3 x$.
A reflection about the x-axis means multiplying the function by $-1$.

Convert the logarithmic inequality to an exponential inequality. Since the base $3 > 1$, the inequality direction remains the same.

For $k(x) = \log_3 x$, the domain requires $x > 0$.
Combining $x \ge 27$ with $x > 0$, the solution is $x \ge 27$.
The values of $x$ are $\boxed{\mathbf{x \ge 27}}$.