Q) f: R -> R, If f(x) = x^2 + x, for all x belongs to R, find whether f(x) is one-one onto or not? this was solved starting with - f''(x) = 2x + 1 and so on... what''s this f''(x)???

f′x=2x+1 means for any real value of x ie R in domain there is one image in codomain ie R

PUT X=1 you get 3

put x=2 you get 5

put x=-1 you get -1

this show that if you take any value from domain you get unique value in range THEREFORE THE FUNCTION IS ONE ONE