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 = -$\sqrt{}y+1$ ?