Question

Need help ASAP please

Answer 1

Answer C:
`f(x)=(x+1)/(x-1)`

Explanation:

Notice that all the functions look like x plus a constant in the numerator, and x minus the same constant in the denominator.

So we can do a general analysis finding the inverse of a function of the form:

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

and finding which value of "a" will make
`f(x)=f^(-1)(x)`

To find the inverse we need to solve for "x" in the equivalent equation:

`y=(x+a)/(x-a) \\y\,(x-a)=x+a\\yx-ya=x+a\\yx-x=a+ya\\x(y-1)=a(1+y)\\x=(a(1+y))/(y-1)`

Then, we see that if
`a=1`, then the expression for
`f(x)=f^(-1)(x)`

Then the function that verifies this condition is:

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