Question

Reprezentati grafic functia liniara f(x+1)+3f(-x)=2x+1

Answer 1

fiind functie liniara , inseamna ca e de forma\
f(x)=ax+b
a(x+1) +b+3(-ax+b)=2x+1,∀x∈R
ax+a+b-3ax+3b=2x+1
-2ax+a+4b=2x+1
identificam coeficientii expresiei de grad1
-2a=2
a+4b=1


a=-1
-1+4b=1
a=-1
4b=2
a=-1
b=1/2

deci f(x) =-x+1/2

verificare
-(x+1)+1/2+3(x+1/2)=2x+1
-x+3x-1+1/2+3/2=2x+1
2x-1/2+3/2=2x+1
2x+1=2x+1 adevarat, bine rezolvat
 garficul , piece of cake, vezi atasamanent