To find the corresponding point on the graph of \( g(x) = 0.6x \) when \( (0.36, 2) \) is on the graph of \( f(x) = \log_{0.6}(x) \), we need to understand the relationship between the two functions.
The point \( (0.36, 2) \) means that when \( x = 0.36 \), \( f(0.36) = 2 \). This implies:
\[ \log_{0.6}(0.36) = 2 \]
From the properties of logarithms, we can rewrite this in exponential form:
\[ 0.6^2 = 0.36 \]
Now, we use this relationship to find a corresponding point for \( g(x) \).
Since \( g(x) = 0.6x \), we can substitute \( x = 2 \) into \( g \) to find the corresponding value of \( y \):
\[ g(2) = 0.6 \cdot 2 = 1.2 \]
Thus, when \( g(x) \) has \( x = 2 \), the corresponding point on \( g \) is:
\[ (2, 1.2) \]
However, among the answer choices provided, none contain \( (2, 1.2) \). Instead, we need to check the implications of the logarithm. The inputs to \( g \) correspond to the output values of \( f \):
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If \( (0.36, 2) \) is a point on \( f \),
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then we look for the equivalent representation:
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\( g(f(0.36)) \) which leads us back to \( g(2) \), and we already calculated what that was, resulting in \( (2, 1.2) \).
However, since the options provided were:
- \( (2, 0.36) \)
- \( (-0.36, -2) \)
- \( (-2, 0.36) \)
- \( (0.36, -2) \)
None of these points correspond directly to the points expected.
To clarify the nature of \( g \) and the transformation, keep in mind that logarithmic functions are typically inversed by exponentiation, while such mappings for linear transformations offering the potential zeros would normally shift the axis.
Despite having \( (2, 1.2) \) as resultant from our calculations, the mismatch against multiple-choice responses suggests an alternate relation postulated between \( f \) and \( g \).
In closing, none of the responses yield proper mapped outputs from the given \( f(x) \). Thus a direct answer available here is not known given current response choices; the correlation computes \( (2, 1.2) \) outside the choice constraints provided.