Question

The point with coordinates (0.125, 3)
lies on the graph of f(x)=log0.5 x.


Determine the coordinates (x,y)
of the corresponding point that lies on the graph of g(x)=0.5^x

Answer 1

To find the corresponding point on the graph of \( g(x) = 0.5^x \) from the point \( (0.125, 3) \) on the graph of \( f(x) = \log_{0.5} x \), we need to understand the relationship between the two functions.

1. The function \( f(x) = \log_{0.5} x \) can be rewritten in terms of exponential functions. The point \( (0.125, 3) \) implies that:

\[
f(0.125) = 3 \quad \text{or} \quad \log_{0.5}(0.125) = 3
\]

This means that:

\[
0.5^3 = 0.125
\]

2. To find the corresponding point on \( g(x) = 0.5^x \), we need to find the value of \( g \) at \( x = 3 \):

\[
g(3) = 0.5^3 = 0.125
\]

3. Since the \( y \)-value corresponds to \( 0.125 \) when \( x = 3 \) for \( g(x) \), the point \( (3, 0.125) \) lies on the graph of \( g(x) \).

Thus, the coordinates of the point on the graph of \( g(x) \) that corresponds to the point \( (0.125, 3) \) on the graph of \( f(x) \) are:

\[
\boxed{(3, 0.125)}
\]