Revision: I can solve these questions but occasionally get stuck, can someone point out the easiest method to check for one-one, onto?

f:[-1,1] - R given by f(x) = x/x + 2 is one-one

Find the inverse of the function f: [-1,1] - range f

@rational

Question

Revision: I can solve these questions but occasionally get stuck, can someone point out the easiest method to check for one-one, onto?

f:[-1,1] -> R given by f(x) = x/x + 2 is one-one

Find the inverse of the function f: [-1,1] -> range f

@rational

rational · Answer

y = x/(x+2)


step1 : swap x and y
x = y/(y+2)

step2 : solve y
x(y+2)  =  y
xy+2x =   y
2x = y(1-x)
2x/(1-x) = y

so the inverse is 2x/(1-x)