Question

If A = {−2,−1, 0,1,2} and f : A $\to$ B is an onto function defined by f (x) = x${}^2$ + x + 1, then find B.

• A. B = {1, 3}
• B. B = {1, 3, 7}
• C. B = {-1,3, 7}
• D. B = {-1,-3, -7}

Answer 1

The correct option is B B = {1, 3, 7}

Given: A = {−2,−1, 0,1,2} and
f (x) = x${}^2$ + x + 1
Now,
f (-2) = (-2)${}^2$ + (-2) + 1
= 3
f (-1) = (-1)${}^2$ + (-1) + 1
= 1
f (0) = 0${}^2$ + 0 + 1
= 1
f (1) = 1${}^2$ + 1 + 1
= 3
f (2) = 2${}^2$ + 2 + 1
= 7
Since, f is an onto function, range of f = B = co-domain of f.
$\therefore$ B = {1, 3, 7}.