Find Range Algebraically

[nycmath]

I need a step by step explanation.

Find the range algebraically.

f(x) = x/(x + 2)

[Eigenvalue]

Rewrite the function as y=[tex]\frac{x}{x+2}[/tex]

Solve for x as a function of y

y(x+2)=x

yx-x=-2y

x(y-1)=-2y

x=[tex]\frac{-2y}{y-1}[/tex]

As y is in the denominator, y-1[tex]\ne[/tex]0

y[tex]\ne[/tex]1

(-infinity, 1) U (1, infinity)

[nycmath]

Rewrite the function as y=[tex]\frac{x}{x+2}[/tex]

Solve for x as a function of y

y(x+2)=x

yx-x=-2y

x(y-1)=-2y

x=[tex]\frac{-2y}{y-1}[/tex]

As y is in the denominator, y-1[tex]\ne[/tex]0

y[tex]\ne[/tex]1

(-infinity, 1) U (1, infinity)

So, the range is {y | y cannot be 1}? Yes?

[Eigenvalue]

Yes. That is a different way it write it

[nycmath]

Yes. That is a different way it write it

Range = x written in terms of y. Yes?