Question

domain and range
F(X)=-x^2+2X+3

Answer 1

\[F \left( x \right)=x^2+2x+3=x^2+2x+1+2=\left( x+1 \right)^2+2\]
domain= all real values
\[range=[2,\infty ) \]

Answer 2

@surjithayer, \(x^2\) is negative

Answer 3

\[F \left( x \right)=-x^2+2x+3=-\left( x^2-2x+1-1 \right)+3=-\left( x-1 \right)^2+4\]
domain is same.
\[Range=(-\infty ,4]\]