Question

For the function f(x) = (8-2x)2 ,find f-1 . Determine whether f-1 is a function.




A.
f-1(x) = ;f-1 is a function


B.
f -1 (x) = ; f-1 is not a function


C.
f-1(x) = ;f-1 is not a function


D.
f-1(x) = ; f-1 is a function

Answer 1

f(x) = (8-2x)2=y
let 's find the inverse is  
 (8-2x)2=y,  (8-2x)=sqrt(y), and -2x=sqrt(y) -8,  finally x= (-1/2)sqrt(y)+4
the inverse is f^-1(y)=(-1/2) √y  + 4, when x=y

the inverse is f^-1(x)=(-1/2) √x  + 4

A:  f-1(x) = ;f-1 is a function

Answer 2

Answer:

$y=\frac{8\pm\sqrt{x}}{2}$

Explanation:

We have been given with a function $f(x)=(8-2x)^2$

We need to find $f^{-1}$

when we find inverse of any function we intechange the variables we will get

$x=(8-2y)^2$ after simplification we will get

$y=\frac{8\pm\sqrt{x}}{2}$

$f^{-1}$ is not a function since, for each value of x there is two values of y.