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
Answers
GPT-4o mini
To find the corresponding point on the graph of \( g(x) = 0.6^x \) when given the point \( (0.36, 2) \) on the graph of \( f(x) = \log_{0.6}(x) \), we need to understand the relationship between these two functions.
The point \( (0.36, 2) \) indicates that when \( x = 0.36 \), \( f(0.36) = 2 \). This means:
\[
\log_{0.6}(0.36) = 2
\]
From this equation, we can rewrite it in exponential form:
\[
0.6^2 = 0.36
\]
Now we need to find the corresponding point on the graph of \( g(x) = 0.6^x \). The function \( g(x) \) introduces a new variable \( x \). When \( x = 2 \) in \( g \), we compute:
\[
g(2) = 0.6^2 = 0.36
\]
Since we are looking for the point on the graph of \( g(x) \), we have:
- \( x = 2 \)
- \( g(2) = 0.36 \)
Thus, the corresponding point on the graph of \( g(x) = 0.6^x \) is:
\[
(2, 0.36)
\]
The final answer is the point **(2, 0.36)**.
The point \( (0.36, 2) \) indicates that when \( x = 0.36 \), \( f(0.36) = 2 \). This means:
\[
\log_{0.6}(0.36) = 2
\]
From this equation, we can rewrite it in exponential form:
\[
0.6^2 = 0.36
\]
Now we need to find the corresponding point on the graph of \( g(x) = 0.6^x \). The function \( g(x) \) introduces a new variable \( x \). When \( x = 2 \) in \( g \), we compute:
\[
g(2) = 0.6^2 = 0.36
\]
Since we are looking for the point on the graph of \( g(x) \), we have:
- \( x = 2 \)
- \( g(2) = 0.36 \)
Thus, the corresponding point on the graph of \( g(x) = 0.6^x \) is:
\[
(2, 0.36)
\]
The final answer is the point **(2, 0.36)**.