To solve for [tex]\(1 \phi (-2)\)[/tex] using the given operator definition, follow these steps:
1. Identify the values of [tex]\(p\)[/tex] and [tex]\(q\)[/tex]. Here, [tex]\(p = 1\)[/tex] and [tex]\(q = -2\)[/tex].
2. Substitute these values into the expression [tex]\(p \phi q = 3p - q\)[/tex].
Now, apply the definition of the operator [tex]\(\phi\)[/tex]:
[tex]\[
1 \phi (-2) = 3(1) - (-2)
\][/tex]
Simplify the expression inside the parentheses:
[tex]\[
1 \phi (-2) = 3 \times 1 + 2
\][/tex]
Continue simplifying:
[tex]\[
1 \phi (-2) = 3 + 2
\][/tex]
Thus, we get:
[tex]\[
1 \phi (-2) = 5
\][/tex]
Therefore, the correct answer is:
C) 5
