Question

Which function is f(x) equal to f^-1(x)?

Answer 1

Answer:

c. f(x) x+1/x-1

Step-by-step explanation:

To answer this question, we need to check each answer one by one until we find the right one.  

y = (x+6)/(x-6)  

switch x and y  

x = (y+6)/(y-6)  

solve for y  

x(y-6) = y+6  

xy - 6x = y+6  

y(x-1) = 6x+6  

y = (6x+6) /(x-1) = 6(x+1)/(x-1)  

f^-1(x) = 6(x+1)/(x-1)  

y = (x+2)/(x-2)  

switch x and y  

x = (y+2)/(y-2)  

solve for y  

x(y-2) = y+2  

xy -2x = y+2  

y(x-1) = 2x+2  

y = (2x+2)/(x-1)  

f^-1(x) = 2(x+1)/(x-1)  

y = (x+1)/(x-1) ------ correct one  

switch x and y  

x = (y+1)/(y-1)  

solve for y  

x(y-1) = y+1  

xy - x = y+1  

y(x-1) = x+1  

y = (x+1)/(x-1)  

f^-1(x) = (x+1)/(x-1)  

f(x) = f^-1(x)

Answer 2

Answer:

C. f(x) = x+1/x-1

Step-by-step explanation:

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

Interchange the x and the y

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

Now, we will solve for y

x(y-1) = y+1

xy - x = y+1

y(x-1) = x+1

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

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

f(x) = f^-1(x)

I hope I helped!

Let me know if you need anything else!

~ Zoe