Question

For which function is f(x) equal to f-1(x)?

a. f(x)=x+6/x-6
b. f(x)=x+2/x-2
c. f(x)=x+1/x-1
d. f(x)=x+5/x-5

Answer 1

Your answer would be C

Answer 2

Part C

Explanation:

Part (i)

`f(x)=(x+6)/(x-6)`

Let f(x)=y

`y=(x+6)/(x-6)`

let us solve the above equation for x and replace y with x in the final result

y(x-6)=x+6

xy-6y=x+6

xy-x=6y+6

taking x and 6 out side the bracket

x(y-1)=6(y+1)

`x=6* (y+1)/(y-1)`

replacing x with y

`y=6* (x+1)/(x-1)`

Hence Inverse not equal to the original function

hence Not true

Part (ii)

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

Let f(x)=y

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

let us solve the above equation for x and replace y with x in the final result

y(x-2)=x+2

xy-2y=x+2

xy-x=2y+2

taking x and 2 out side the bracket

x(y-1)=2(y+1)

`x=2* (y+1)/(y-1)`

replacing x with y

`y=2* (x+1)/(x-1)`

Hence Inverse not equal to the original function

hence Not true

Part (iii)

`f(x)=(x+1)/(x-1)`

Let f(x)=y

`y=(x+1)/(x-1)`

let us solve the above equation for x and replace y with x in the final result

y(x-1)=x+1

xy-y=x+1

xy-x=y+1

taking x and 1 out side the bracket

x(y-1)=1(y+1)

`x= (y+1)/(y-1)`

replacing x with y

`y= (x+1)/(x-1)`

Hence Inverse equal to the original function

hence true