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 answer

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).