Verified Answer :

HomertheGenius

f ( x ) = ( x - 1 ) / 2
y = ( x - 1 ) / 2
x - 1 = 2 y
x = 2 y + 1
f ^(-1) ( x ) = 2 x + 1  ( this is inverse function )
f ^(-1) ( 5 ) = 2 * 5 + 1 = 10 + 1 = 11
Answer: C ) 11 

calculista

Answer:

\(f^{-1}(5)=11\)

Step-by-step explanation:

Step 1

Find the inverse function

we have

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

Let

\(y=f(x)\)

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

Exchanges the variables x for y and y for x

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

Isolate the variable y

\(y=2x+1\)

Let

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

\(f^{-1}(x)=2x+1\) ------> inverse function

Step 2

Find \(f^{-1}(5)\)

Substitute the value of \(x=5\) in the inverse function

\(f^{-1}(5)=2(5)+1=11\)

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