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 ?(1 point) Responses (0.36, -2) (0.36, -2) (-0.36, -2) (-0.36, -2) (-2, 0.36) (-2, 0.36) (2, 0.36)
Answers
GPT-4o mini
To find the corresponding point on the graph of \( g(x) = 0.6^x \), we start with the given point on the graph of \( f(x) = \log_{0.6}(x) \), which is \( (0.36, 2) \). This means that \( f(0.36) = 2 \).
We know the relationship between the logarithmic function and its corresponding exponential function. The statement \( \log_{0.6}(0.36) = 2 \) means that \( 0.6^2 = 0.36 \).
Now, we can find the corresponding point for \( g(x) \):
1. Since \( g(x) = 0.6^x \) and we know \( x = 2 \) corresponds to \( y = 0.36 \):
\[ g(2) = 0.6^2 = 0.36 \]
Thus, the corresponding point on the graph of \( g(x) \) is:
\[ (2, 0.36) \]
Therefore, the answer is:
**(2, 0.36)**.
We know the relationship between the logarithmic function and its corresponding exponential function. The statement \( \log_{0.6}(0.36) = 2 \) means that \( 0.6^2 = 0.36 \).
Now, we can find the corresponding point for \( g(x) \):
1. Since \( g(x) = 0.6^x \) and we know \( x = 2 \) corresponds to \( y = 0.36 \):
\[ g(2) = 0.6^2 = 0.36 \]
Thus, the corresponding point on the graph of \( g(x) \) is:
\[ (2, 0.36) \]
Therefore, the answer is:
**(2, 0.36)**.