Respuesta :

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:

[tex]f^{-1}(5)=11[/tex]

Step-by-step explanation:

Step 1

Find the inverse function

we have

[tex]f(x)=\frac{x-1}{2}[/tex]

Let

[tex]y=f(x)[/tex]

[tex]y=\frac{x-1}{2}[/tex]

Exchanges the variables x for y and y for x

[tex]x=\frac{y-1}{2}[/tex]

Isolate the variable y

[tex]y=2x+1[/tex]

Let

[tex]f^{-1}(x)=y[/tex]

[tex]f^{-1}(x)=2x+1[/tex] ------> inverse function

Step 2

Find [tex]f^{-1}(5)[/tex]

Substitute the value of [tex]x=5[/tex] in the inverse function

[tex]f^{-1}(5)=2(5)+1=11[/tex]

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