If f(x)=2/(x+1), then what is the value of f^-1(1/5)?

Ah an inverse question.

set f(x) as y for simplicity.

y = 2/(x+1), the goal for finding the inverse of the function is to isolate x, so the first step: yx + y = 2. 

next, move y to the right hand side to reach yx = 2 - y. 

finally, divide y over to the right hand side to reach x = (2-y)/y

Now as the core concept of the inverse, we switch the positions of x and y by the time we reach this step.

y = (2-x)/x, and plug in 1/5 to get y = (2-1/5)/(1/5) and that is 9/5 * 5 = 9 

You may also find the avlue of x by setting 2/(x+1) = 1/5 and solve x from there.