Răspuns:
[√(f (2013))]=[√(2015*2016)]=2015
Explicație pas cu pas:
f:R → R, f(x) = x²+5x+6.
Se cere [√(f (2013))], unde [a ] reprezintă partea întreaga a numărului real a.
f (2013)=2013²+5*2013+6
f(x)=2013²+2*2013+3*2013+6
f(2013)=2013(2013+2)+3(2013+2)
f(2013)= 2013*2015+3*2015
f(2013)=2015(2013+3)
f(2013)=2015*2016
√f(2013)=√(2015*2016)
√2015²<√(2015*2016)< √2016²
2015<√(2015*2016)<2016
=> [√(f (2013))]=[√(2015*2016)]=2015
