AP EAPCET 08-Jul-2022 Shift 2 Paper

Given, f(x)=x|x|=[

x(x),x≥0

x(−x),x<0

]

⇒ f(x)=[

x2,x≥0

−x2,x<0

] Also, f:R→R

According to the graph-
domain‌of‌f(x)=Range‌of‌f(x)=R
∴Range=Codomain=R
⇒ f(x) is an onto function.
If a line parallel to X−axis is drawn, it will intersects at only one point of f(x)
Hence, f(x) is one-one also.