Question

The table below shows select values of the function ff, which is odd and whose domain is all real numbers. Find f, of, 7f(7).
xx −14, −10, −7, 4, 8 , 9
f, of, xf(x) 18, −7, −19 , -13, 7, 4

Answer 1

To solve for \( f(7) \) and \( 7f(7) \), given that \( f \) is an odd function and we have some values from the function, we can use the properties of odd functions.

An odd function satisfies the property:

\[
f(-x) = -f(x)
\]

From the provided values:

- \( f(-14) = 18 \) implies \( f(14) = -18 \)
- \( f(-10) = -7 \) implies \( f(10) = 7 \)
- \( f(-7) = -19 \) implies \( f(7) = 19 \)
- \( f(4) = -13 \)
- \( f(8) = 7 \)
- \( f(9) = 4 \)

Now we need to find \( f(7) \):

\[
f(7) = 19
\]

Next, we calculate \( 7f(7) \):

\[
7f(7) = 7 \cdot 19 = 133
\]

Therefore, the final answer is:

\[
f(7) = 19 \quad \text{and} \quad 7f(7) = 133
\]