The range of the function f(x) = (x+2)/|x+2|,x ≠ -2 is A. {-1, 1} B. {-1, 0, 1} C. {1} D. (0, ∞)

Question

The range of the function f(x) = \(\frac{x+2}{|x+2|}\),x ≠ -2 is

A. {-1, 1} 

B. {-1, 0, 1} 

C. {1} 

D. (0, ∞)

Answer 1

Option : (A)

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

When x>-2,

We have,

f(x) = \(\frac{x+2}{x+2}\) 

= 1 

When x<-2, 

We have,

f(x) = \(\frac{x+2}{-(x+2)}\) 

= -1 

R(f) = {-1, 1}