Question

Find the range of the function f(x)= x+2/ |x+2| , x≠-2.

Answer 1

The domain of the function is  

(

−

∞

,

2

)

∪

(

2

,

+

∞

)

.

We can simplify in this way:

y

=

(

x

−

2

)

(

x

+

2

)

x

−

2

=

x

+

2

.

Since the range of  

y

=

x

+

2

is  

R

, seems that the range is  

R

, but we have that  

x

≠

2

so the range is  

y

≠

4

, because the graph is a line without the point  

P

(

2

,

4

)

.

graph{(x^2-4)/(x-2) [-10, 10, -5, 5]}