Prove without using calculus that the following function is

Prove (without using calculus) that the following function is one-to-one throughout its domain.

Is this function onto?

Prove (without using calculus) that the following function is one-to-one throughout its domain. f(x) = x-2/x-1 Is this function onto?

Solution

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

f(x)=f(y) implies

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

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

x-1=y-1

x=y

Hence f is one to one

Let y =f(x)

y=1-1/(x-1)

1-y=1/(x-1)

x-1=1/(1-y)

x=1+1/(1-y)

So we can find an x except for y=1

So f is not onto as f(x) is not equal to 1 for any x