Question
the point ( 0.36, 2) lies on the graph of f(x) = log0.6 x. what is the corresponding point on the graph of g(x) = 0.6^x
Answers
GPT-4o mini
To find the corresponding point on the graph of \( g(x) = 0.6^x \), we first need to recognize the relationship between the logarithmic function \( f(x) = \log_{0.6}(x) \) and the exponential function \( g(x) = 0.6^x \).
Given that the point \( (0.36, 2) \) lies on the graph of \( f(x) \), this means:
\[
f(0.36) = \log_{0.6}(0.36) = 2
\]
This implies that:
\[
0.6^2 = 0.36
\]
To find the corresponding point on \( g(x) \), we note that if \( (a, b) \) is a point on \( f(x) \), then the corresponding point \( (b, a) \) will be a point on \( g(x) \).
Since \( f(0.36) = 2 \), the corresponding point on the graph of \( g(x) = 0.6^x \) will be:
\[
(2, 0.36)
\]
Thus, the corresponding point on the graph of \( g(x) \) is \( (2, 0.36) \).
Given that the point \( (0.36, 2) \) lies on the graph of \( f(x) \), this means:
\[
f(0.36) = \log_{0.6}(0.36) = 2
\]
This implies that:
\[
0.6^2 = 0.36
\]
To find the corresponding point on \( g(x) \), we note that if \( (a, b) \) is a point on \( f(x) \), then the corresponding point \( (b, a) \) will be a point on \( g(x) \).
Since \( f(0.36) = 2 \), the corresponding point on the graph of \( g(x) = 0.6^x \) will be:
\[
(2, 0.36)
\]
Thus, the corresponding point on the graph of \( g(x) \) is \( (2, 0.36) \).