Question

an equation that defines y as a function of x is given. solve for y in terms of x, and replace y with the function notation f(x)
x - 2y = 12
oa. f(x)= -\frac{1}{2}x + 6
ob. f(x)= -x + 6
oc. f(x)= \frac{1}{2}x - 6
od. f(x)= \frac{1}{2}x - 12

Explanation:

Step1: Start with the given equation

We have the equation \( x - 2y = 12 \). Our goal is to solve for \( y \) in terms of \( x \).

Step2: Isolate the term with \( y \)

Subtract \( x \) from both sides of the equation: \( -2y = -x + 12 \).

Step3: Solve for \( y \)

Divide every term by \( -2 \): \( y=\frac{-x + 12}{-2}=\frac{1}{2}x-6 \).

Step4: Replace \( y \) with \( f(x) \)

Since \( y = f(x) \), we get \( f(x)=\frac{1}{2}x - 6 \).

Answer:

C. \( f(x)=\frac{1}{2}x - 6 \)