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HELP (I WILL GIVE 30 POINTS)
For the function f(x) = (8-­2x)2 ,find f-­1 . Determine whether f­-1 is a function.

answer choices:
f­-1(x) = ±8+x2−−−√; f­-1 is a function


f­-1(x) = ±8+x2−−−√; f­-1 is not a function


f­-1(x) = 8±x√2; f­-1 is not a function


f­-1(x) = 8±x√2; f­-1 is a function

Respuesta :

wegnerkolmp2741o

Answer:

4 ± 1/2sqrt(x) = y

This is not a function

Step-by-step explanation:

f(x) = (8-2x)^2

y = (8-2x)^2

To find the inverse function, exchange x and y and then solve for y

x = (8-2y)^2

Take the square root of each side

±sqrt(x) = 8-2y

Subtract 8 from each side

-8±sqrt(x) = 8-8-2y

-8±sqrt(x) = -2y

Divide by -2

-8/-2±  1/2sqrt(x) = -2/-2y

4 ± 1/2sqrt(x) = y

This is not a function

phyozayaraung4

I think is (A)

> x = (8 - 2f^-1(x))²

=> x^(½) = 8 - 2f^-1(x).

=> -2f^-1(x) = 8 - √x

Therefore:

f^-1(x) = (8 - √x)/2

Hope this help

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