Question

Let the function be f : R ---> R be defined as f(x) = 2x + sinx , x belongs to R.
then f is
a. one-one and onto
b. one-one but not onto
c. onto but not one-one
d. neither one-one nor onto

Answer 1

Answer:

(a) one- one and onto

Step-by-step explanation:

since -1≤ sinx ≤ 1. x€R

=> 2x+sinx has an unique value for every x €R

=> f is one- one

also x€R => 2x+sinx€R

=> f is onto

hence option (a) is correct, f is one-one and onto