Sure, let's solve this step-by-step and express the given equation in the proper function notation with [tex]\(c\)[/tex] as the independent variable.
Given Equation:
[tex]\[ 6c = 2p - 10 \][/tex]
We need to solve this equation for [tex]\(p\)[/tex] in terms of [tex]\(c\)[/tex].
Step 1: Isolate the [tex]\(2p\)[/tex] term.
[tex]\[ 6c + 10 = 2p \][/tex]
Step 2: Solve for [tex]\(p\)[/tex] by dividing both sides by 2.
[tex]\[ p = 3c + 5 \][/tex]
Now, we need to write this in function notation. Since [tex]\(c\)[/tex] is the independent variable and we have [tex]\(p\)[/tex] expressed in terms of [tex]\(c\)[/tex], we can rewrite the equation in the form [tex]\(f(c) = 3c + 5\)[/tex].
However, we notice that the function notation given in the choices involves [tex]\(p\)[/tex], so let's revise our approach.
Revisiting the choices:
- This suggests that we express function in terms of [tex]\(f(p)\)[/tex].
Given that we have [tex]\(p = 3c + 5\)[/tex], we can restate that:
[tex]\[ p \to 3c + 5 \][/tex]
Therefore, the fourth option,
[tex]\[ f(p) = 3c + 5 \][/tex]
is the one that correctly represents the equation in function notation where [tex]\(c\)[/tex] is the independent variable.
So, the answer is:
[tex]\[ f(p) = 3c + 5 \][/tex]
