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Answer:

Option C \(f^{-1}(x)=2(x+6)\)

Step-by-step explanation:

we have that

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

Let

\(y=f(x)\)

\(y=\frac{1}{2}x-6\)

Exchange the variables x for y and y for x

\(x=\frac{1}{2}y-6\)

Isolate the variable y

\(x+6=\frac{1}{2}y\)

\(y=2(x+6)\)

Let

\(f^{-1}(x)=y\)

\(f^{-1}(x)=2(x+6)\)

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