Very simple applications' issue

[Andrax]

Homework Statement

so i want to prove that an application is bijective
y \geq 1we're looking for an x\geq-2 : y= f(x)
anyway at the end
i have lx+2l=\sqrt{}y+1
the teached said x = \sqrt{}y+1-2 without studying the other case
Ps: the +1 is includedi nthe square root

Homework Equations

The Attempt at a Solution

the other case lx+2l=\sqrt{}y+1
x+2=\sqrt{}y+1 or x+2=-\sqrt{}y+1

the second x is going to be <2 so we can exclude it the first x is going to be >2 we're oging to use it , but why our teacher didn't study the second case in which x+2 = -\sqrt{}y+1 ?

 

[Mark44]

Homework Statement

so i want to prove that an application is bijective
y \in \left[1(y >=1)+\infty\left[ we're looking for an x from \left[-2+\infty\left[(x>=-2) : y= f(x)
anyway at the end
i have lx+2l=\sqrt{}y+1
the teached said x = \sqrt{}y+1-2 without studying the other case
Ps: the +1 is includedi nthe square root

Homework Equations

Your LaTeX is broken, so I can't understand what you have attempted to write.

The Attempt at a Solution

the other case lx+2l=\sqrt{}y+1
x+2=\sqrt{}y+1 or x+2=-\sqrt{}y+1

the second x is going to be <2 so we can exclude it the first x is going to be >2 we're oging to use it , but why our teacher didn't study the second case in which x+2 = -\sqrt{}y+1 ?