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The problem asks to write a function \( g(x) \) whose graph represents a reflection in the \( y \)-axis of the graph of \( f(x) = \ln(x) - 2 \).

### Solution:

To reflect a function across the \( y \)-axis, you replace \( x \) with \( -x \) in the function. So, for the function \( f(x) = \ln(x) - 2 \), reflecting it across the \( y \)-axis gives:

\[
g(x) = f(-x) = \ln(-x) - 2
\]

Thus, the reflected function is:

\[
g(x) = \ln(-x) - 2
\]

Note that this new function, \( g(x) = \ln(-x) - 2 \), is only defined for \( x < 0 \), since the natural logarithm, \( \ln(x) \), is only defined for positive values of \( x \), and \( -x \) must be positive.

Would you like any further details or have questions?

### Relative Questions:
1. What is the domain of the function \( g(x) = \ln(-x) - 2 \)?
2. How does the reflection of a function affect its graph visually?
3. What is the inverse of \( f(x) = \ln(x) - 2 \)?
4. How would you translate \( f(x) = \ln(x) - 2 \) instead of reflecting it?
5. What happens if you reflect the function across the \( x \)-axis instead?

### Tip:
When reflecting a function across the \( y \)-axis, remember to replace \( x \) with \( -x \) in the equation of the function.

Write a function g whose graph represents a reflection in the y-axis of the graph of f(x) = ln(x) - 2. g(x) = ?

Learn how to reflect the function f(x) = ln(x) - 2 across the y-axis. This problem covers key algebraic concepts and transformations, including the formula g(x) = f(-x). Suitable for students in Grades 9-12.

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