Question

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

Answer 1

Answer:

$f(x)= 2x$

Step-by-step 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)

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

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

$-y= \frac{2}{x}$

$-x= \frac{2}{y}$,  cross multiply it

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

$-y= \frac{2}{x}$, 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

$\frac{x}{2}=y$,  Inverse is not equal to f(x)

Answer 2

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