Question

Given is the graph of the function h(x)=log1/2 x . Which of the following correctly uses the graph to find h(1)+h^−1(−1)
?

(1 point)
Responses

h(1)+h−1(−1)=3
h left parenthesis 1 right parenthesis plus h superscript negative 1 baseline left parenthesis negative 1 right parenthesis equals 3

h(1)+h−1(−1)=2.5
h left parenthesis 1 right parenthesis plus h superscript negative 1 baseline left parenthesis negative 1 right parenthesis equals 2.5

h(1)+h−1(−1)=2
h left parenthesis 1 right parenthesis plus h superscript negative 1 baseline left parenthesis negative 1 right parenthesis equals 2

h(1)+h−1(−1)=0

Answer 1

To find \( h(1) + h^{-1}(-1) \) using the graph of the function \( h(x) = \log_{1/2}(x) \), we first need to determine the value of \( h(1) \) and then find \( h^{-1}(-1) \).

1. **Calculating \( h(1) \)**:
The function \( h(x) = \log_{1/2}(x) \) can be evaluated at \( x = 1 \):
\[
h(1) = \log_{1/2}(1)
\]
Since \( \log_{a}(1) = 0 \) for any positive \( a \):
\[
h(1) = 0
\]

2. **Finding \( h^{-1}(-1) \)**:
To find \( h^{-1}(-1) \), we need to determine \( x \) such that:
\[
h(x) = -1
\]
Therefore, we solve the equation:
\[
\log_{1/2}(x) = -1
\]
Rewriting this in exponential form gives:
\[
x = (1/2)^{-1} = 2
\]
Hence, \( h^{-1}(-1) = 2 \).

3. **Combining the results**:
Now we can find \( h(1) + h^{-1}(-1) \):
\[
h(1) + h^{-1}(-1) = 0 + 2 = 2
\]

Therefore, the correct answer is:
\[
h(1) + h^{-1}(-1) = 2
\]