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Consider the function represented by the equation [tex]\(6c = 2p - 10\)[/tex]. Write the equation in function notation, where [tex]\(c\)[/tex] is the independent variable.

A. [tex]\(f(c) = \frac{1}{3} p + \frac{5}{3}\)[/tex]

B. [tex]\(f(c) = 3c + 5\)[/tex]

C. [tex]\(f(p) = \frac{1}{3} p + \frac{5}{3}\)[/tex]

D. [tex]\(f(p) = 3c + 5\)[/tex]

Sagot :

GinnyAnswer
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]
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