Question

For which function is f(x) not equal to f-1(x)?

A- f(x)=2-x
B-f(x)=2/x
C=f(x)=-x
D=f(x)=2x

Answer 1

D is the answer.
If f(x) or y = 2x, the inverse is x = 2y or y=x/2 which is not f(x).

Answer 2

`f(x)= 2x`

Explanation:

For which function is f(x) not equal to f^-1(x)

LEts check with each function, we find out inverse for each option

`f(x)= 2-x`

Replace f(x) by y, then switch the variables and solve for y

`y= 2-x`

`x= 2-y`, Add y on both sides

`x+y= 2`, Subtract x from both sides

`y= 2-x`, Inverse is equal to f(x)

`-f(x)= (2)/(x)`

Replace f(x) by y, then switch the variables and solve for y

`-y= (2)/(x)`

`-x= (2)/(y)`, cross multiply it

`-xy = 2`, divide by x on both sides

`-y= (2)/(x)`, Inverse is equal to f(x)

`f(x)= -x`

Replace f(x) by y, then switch the variables and solve for y

`y= -x`

`x=-y`, Add y on both sides

`x+y= 0`, Subtract x from both sides

`y=-x`, Inverse is equal to f(x)

`f(x)= 2x`

Replace f(x) by y, then switch the variables and solve for y

`y= 2x`

`x= 2y`, divide by 2 on both sides

`(x)/(2)=y`, Inverse is not equal to f(x)