Select the correct answer. For which function is f (x) not equal to f - 1 (x) ?

A. f (x) = 2-x

B. f (x) = -x

C. f (x) = 2x

D. f (x) = 2/x

A.

f (x) = 2-x

let us find f⁻¹ (x)

let us say f (x) = y

y=2-x

now we switch x as y and y as x

x=2-y

solve for y

y=2-x

f⁻¹ (x) = 2-x

so here f (x) and f⁻¹ (x) are same

B.

f (x) = -x

let us find f⁻¹ (x)

let us say f (x) = y

y=-x

now we switch x as y and y as x

x=-y

solve for y

y=-x

f⁻¹ (x) = -x

so here f (x) and f⁻¹ (x) are same

C.

f (x) = 2x

let us find f⁻¹ (x)

let us say f (x) = y

y=2x

now we switch x as y and y as x

x=2y

solve for y

y=x/2

f⁻¹ (x) = x/2

so here f (x) and f⁻¹ (x) are not same

D.

f (x) = 2/x

let us find f⁻¹ (x)

let us say f (x) = y

y=2/x

now we switch x as y and y as x

x=2/y

solve for y

y=2/x

f⁻¹ (x) = 2/x

so here f (x) and f⁻¹ (x) are same

A is the answer for which function f (x) is t equal to f - 1 (x)