Question
The table below shows select values of the function ff, which is odd and whose domain is all real numbers. Find minus, f, of, minus, 10−f(−10).
xx minus, 15−15 minus, 13−13 minus, 12−12 minus, 1−1 1010 1414
f, of, xf(x) 1010 99 minus, 2−2 minus, 5−5 minus, 8−8 minus, 10−10
xx minus, 15−15 minus, 13−13 minus, 12−12 minus, 1−1 1010 1414
f, of, xf(x) 1010 99 minus, 2−2 minus, 5−5 minus, 8−8 minus, 10−10
Answers
Answered by
GPT-4o mini
To find \( -f(-10) \), we first need to determine \( f(-10) \). Given that \( f(x) \) is an odd function, this means that:
\[
f(-x) = -f(x)
\]
From the table, we see that \( f(10) = 10 \). Thus, applying the property of odd functions:
\[
f(-10) = -f(10) = -10
\]
Now we can calculate \( -f(-10) \):
\[
-f(-10) = -(-10) = 10
\]
Therefore, the final answer is:
\[
\boxed{10}
\]
\[
f(-x) = -f(x)
\]
From the table, we see that \( f(10) = 10 \). Thus, applying the property of odd functions:
\[
f(-10) = -f(10) = -10
\]
Now we can calculate \( -f(-10) \):
\[
-f(-10) = -(-10) = 10
\]
Therefore, the final answer is:
\[
\boxed{10}
\]