To express the given equation, [tex]\( 6c = 2p - 10 \)[/tex], in function notation where [tex]\( c \)[/tex] is the independent variable, follow these steps:
1. Rewrite the equation to isolate [tex]\( p \)[/tex]:
[tex]\[
6c = 2p - 10
\][/tex]
Add 10 to both sides to isolate the term involving [tex]\( p \)[/tex]:
[tex]\[
6c + 10 = 2p
\][/tex]
2. Solve for [tex]\( p \)[/tex]:
Divide both sides by 2 to solve for [tex]\( p \)[/tex]:
[tex]\[
p = \frac{6c + 10}{2} = 3c + 5
\][/tex]
3. Write the solution in function notation:
Knowing that [tex]\( p = f(c) \)[/tex], rewrite the expression obtained in the previous step as:
[tex]\[
f(c) = 3c + 5
\][/tex]
Thus, the correct function notation for the given equation [tex]\( 6c = 2p - 10 \)[/tex], where [tex]\( c \)[/tex] is the independent variable, is:
[tex]\[ f(c) = 3c + 5 \][/tex]
Hence, the correct choice from the given options is:
[tex]\[ f(c) = 3c + 5 \][/tex]
