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

Question

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

c...to show this, interchange letters: x = (y+1)/(y-1)

xy-x = y + 1

xy - y) = x + 1

y(x-1) = x+1

y = (x+1)/(x-1) ⇐ this is f^-1(x) and it's identical to f(x). 

 

Note: the equal sign is missing in the definitions of the functions c. & d.

Answer 2

Here is how you do the first problem.

 

Write f(x) = y = (x+6)/(x-6)  Switch x for y and y for x and write

 

x= (y+6)/(y-6)  Multiply both sides  by ( y-6 )  You have

 

xy - 6x  =  y + 6  Subtact y from both sides and add 6x to both sides

 

xy - y = 6x + 6  Factor out y on the left side

 

y(x-1)  =  (6x+6)   Divide both sides by (x-1) yielding 

 

y = (6x+6)/(x-1)  This nis your inverse function.  It's a substitution of x for y and visa versa and some algebra Not hard at all