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
?(1 point)
Responses

(2, 0.36)
(2, 0.36)

(-0.36, -2)
(-0.36, -2)

(-2, 0.36)
(-2, 0.36)

(0.36, -2)

Answer 1

To find the corresponding point on the graph of \( g(x) = 0.6^x \) based on the point \( (0.36, 2) \) that lies on the graph of \( f(x) = \log_{0.6}(x) \), we need to understand the relationship between these two functions.

From the properties of logarithms, if \( f(a) = b \) for \( f(x) = \log_{0.6}(x) \), then it follows that:

\[
0.6^b = a
\]

Given the point \( (0.36, 2) \), we have:
- \( b = 2 \)
- \( a = 0.36 \)

Thus, we can write:

\[
0.6^2 = 0.36
\]

Now we want the corresponding point on the graph of \( g(x) \):

Using the relationship confirmed above, we know that \( g(2) = 0.6^2 = 0.36 \).

So the corresponding point on the graph of \( g(x) = 0.6^x \) is:

\[
(2, 0.36)
\]

Thus, the correct response is:

**(2, 0.36)**