To determine the value of [tex]\( x \)[/tex] for which [tex]\( f(x) = 7 \)[/tex] in the function [tex]\( f = \{(8,3), (-3,9), (1,7), (-4,4)\} \)[/tex], follow these steps:
1. Understand that the function [tex]\( f \)[/tex] is given as a set of ordered pairs [tex]\((x, f(x))\)[/tex].
2. Identify the ordered pair where the second component (which represents the function's output, [tex]\( f(x) \)[/tex]) is equal to 7.
Let's examine each pair:
- For the pair [tex]\((8, 3)\)[/tex], the second component is 3, which is not equal to 7.
- For the pair [tex]\((-3, 9)\)[/tex], the second component is 9, which is not equal to 7.
- For the pair [tex]\((1, 7)\)[/tex], the second component is 7, which matches our requirement.
- For the pair [tex]\((-4, 4)\)[/tex], the second component is 4, which is not equal to 7.
The ordered pair that satisfies the condition [tex]\( f(x) = 7 \)[/tex] is [tex]\((1, 7)\)[/tex].
Thus, the value of [tex]\( x \)[/tex] for which [tex]\( f(x) = 7 \)[/tex] is [tex]\( 1 \)[/tex].
Therefore, the value of [tex]\( x \)[/tex] is [tex]\(\boxed{1}\)[/tex].
