Question

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

Answer 1

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

Answer 2

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