##F(x)=(m²-m+1)x+3## . Find ##m in RR## if the function is strictly increasing . Thank you very much . Sorry for bad English it is not my mother tongue . ?

##F(x)## is strictly increasing for any ##m in RR##...

Note that:

##m^2+m+1 = m^2+2(1/2)m+1/4+3/4##

##color(white)(m^2+m+1) = (m+1/2)^2+3/4 >= 3/4## for any ##m in RR##

Hence ##F(x)## is the equation of a line with positive , thus strictly increasing.