Respuesta :

Bria161
Your answer would be C
Cricetus

Answer:

Part C

Step-by-step explanation:

Part (i)

[tex]f(x)=\frac{x+6}{x-6}[/tex]

Let f(x)=y

[tex]y=\frac{x+6}{x-6}[/tex]

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)

[tex]x=6\times \frac{y+1}{y-1}[/tex]

replacing x with y

[tex]y=6\times \frac{x+1}{x-1}[/tex]

Hence Inverse not equal to the original function

hence Not true

Part (ii)

[tex]f(x)=\frac{x+2}{x-2}[/tex]

Let f(x)=y

[tex]y=\frac{x+2}{x-2}[/tex]

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)

[tex]x=2\times \frac{y+1}{y-1}[/tex]

replacing x with y

[tex]y=2\times \frac{x+1}{x-1}[/tex]

Hence Inverse not equal to the original function

hence Not true

Part (iii)

[tex]f(x)=\frac{x+1}{x-1}[/tex]

Let f(x)=y

[tex]y=\frac{x+1}{x-1}[/tex]

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)

[tex]x= \frac{y+1}{y-1}[/tex]

replacing x with y

[tex]y= \frac{x+1}{x-1}[/tex]

Hence Inverse equal to the original function

hence true

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