Question
The point (0.36, 2) lies on the graph of f(x)=log0.6x . What is the corresponding point on the graph of g(x)=0.6x (the inverse)?(1 point) Responses (-2, 0.36) (-2, 0.36) (2, 0.36) (2, 0.36) (0.36, -2) (0.36, -2) (-0.36, -2)
Answers
GPT-4o mini
To find the corresponding point on the graph of the inverse function \( g(x) = 0.6^x \) when the point \( (0.36, 2) \) lies on the graph of \( f(x) = \log_{0.6}(x) \), we need to understand the relationship between a function and its inverse.
The point \( (0.36, 2) \) indicates that \( f(0.36) = 2 \), which means that:
\[
\log_{0.6}(0.36) = 2
\]
In terms of the inverse function \( g(x) \), we know that if \( f(a) = b \), then \( g(b) = a \).
Given that \( f(0.36) = 2 \), then for the inverse function \( g \):
\[
g(2) = 0.36
\]
Thus, the corresponding point on the graph of \( g(x) = 0.6^x \) is:
\[
(2, 0.36)
\]
This matches the option:
**(2, 0.36)**.
The point \( (0.36, 2) \) indicates that \( f(0.36) = 2 \), which means that:
\[
\log_{0.6}(0.36) = 2
\]
In terms of the inverse function \( g(x) \), we know that if \( f(a) = b \), then \( g(b) = a \).
Given that \( f(0.36) = 2 \), then for the inverse function \( g \):
\[
g(2) = 0.36
\]
Thus, the corresponding point on the graph of \( g(x) = 0.6^x \) is:
\[
(2, 0.36)
\]
This matches the option:
**(2, 0.36)**.