Question

consider the function f:R=R defined as f(x)=x/x^2+1​

Answer 1

Answer:

what we should do in the question

Answer 2

Answer:

Consider the function f : R → R defined by f ( x ) = { ( 2 − s i n ( 1 x ) ) | x | , x ≠ 0 0 , x = 0 f(x)={(2−sin(1x))|x|,x≠00,x=0 (1) monotonic on  ( − ∞ , 0 ) ∪ ( 0 , ∞ ) (−∞,0)∪(0,∞) (2) not monotonic on  ( − ∞ , 0 ) (−∞,0) and  ( 0 , ∞ ) (0,∞) (3) monotonic on  ( 0 , ∞ ) (0,∞) only (4) monotonic on  ( − ∞ , 0 ) (−∞,0)