Question

the table below shows select values of the function f, which is odd and whose domain is all real numbers. find f(2).

x	-13	-11	-9	-2	-1	6
f(x)	-2	4	-3	-5	2	2

answer attempt 1 out of

Explanation:

Step1: Recall the property of odd functions

For an odd function \( f \), the property is \( f(-x)= -f(x) \), which can be rearranged to \( f(x)= -f(-x) \).

Step2: Apply the property to find \( f(2) \)

We need to find \( f(2) \). Using the odd function property, \( f(2)= -f(-2) \). From the table, when \( x = - 2 \), \( f(-2)=-5 \). So we substitute \( f(-2) \) into the formula: \( f(2)=-(-5) = 5 \).

Answer:

\( 5 \)