Question

If f:R to A given by f(x) =x^2 +2x+2 is onto function , find set A

Answer 1

We have
f(x)=
x
2
−2x+2
=
x
2
−2x+1+1
f(x)=
(x−1)
2
+1
Minimum value occurs when perfect square
term becomes 0 i.e. at x=1
f
(x)
min
=0+1=1
Max value will tend toward ∞.
Hence range is [1,∞)
Codomain=A
For onto function
Codomain=Range
A=[1,∞)