Question

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

Answer 1

Answer:

Part C

Step-by-step explanation:

Part (i)

$f(x)=\frac{x+6}{x-6}$

Let f(x)=y

$y=\frac{x+6}{x-6}$

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)

$x=6\times \frac{y+1}{y-1}$

replacing x with y

$y=6\times \frac{x+1}{x-1}$

Hence Inverse not equal to the original function

hence Not true

Part (ii)

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

Let f(x)=y

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

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)

$x=2\times \frac{y+1}{y-1}$

replacing x with y

$y=2\times \frac{x+1}{x-1}$

Hence Inverse not equal to the original function

hence Not true

Part (iii)

$f(x)=\frac{x+1}{x-1}$

Let f(x)=y

$y=\frac{x+1}{x-1}$

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)

$x= \frac{y+1}{y-1}$

replacing x with y

$y= \frac{x+1}{x-1}$

Hence Inverse equal to the original function

hence true

Answer 2

Your answer would be C