A function f : `A to B`, where `A={x:-1 le x le 1}` and `B={y:1 le y le 2}` is defined by the rule `y=f(x)=1+x^(2)`. Which of the following statement is correct ?

Options

A. f is injective but not surjective
B. f is surjective but not injective
C. f is both injecitve and surjective
D. f is neither injective nor surjective

Answer

B

Explanation

Since, `A={x:-1lex le1}" and "B={y:-leyle2}`
Aos, `" "y=f(x)=1=x^(2)`
For `" "x=-1,y=1+(-1)^(2)=2`
and for `" "x=1,y=1+1^(2)=2`
Thus, f is not injective (one-one)
Here, for all B, there is a pre-image.
Hence, f is surjective.