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)
left parenthesis 0.36 comma negative 2 right parenthesis

(−2,0.36)
left parenthesis negative 2 comma 0.36 right parenthesis

(−0.36,−2)
left parenthesis negative 0.36 comma negative 2 right parenthesis

(2,0.36)

Answer 1

To find the corresponding point on the graph of \( g(x) = 0.6^x \) based on the point \( (0.36, 2) \) on the graph of \( f(x) = \log_{0.6}(x) \), we need to note how the two functions are related.

The point \( (0.36, 2) \) means that \( f(0.36) = 2 \). Since \( f(x) = \log_{0.6}(x) \), this implies that:
\[
0.6^2 = 0.36.
\]

Now we need to find the point for \( g(x) = 0.6^x \) that corresponds to \( f(0.36) = 2 \). The logarithm and exponential functions are inverses of each other, meaning if \( \log_{b}(a) = c \), then \( b^c = a \).

So if \( f(0.36) = 2 \), it follows that in the context of \( g(x) \):
\[
g(2) = 0.6^2 = 0.36.
\]

Thus, the corresponding point on the graph of \( g(x) \) is \( (2, 0.36) \).

The correct response is:
\[
(2, 0.36).
\]