Question

sa se determine functia de gradul I , f:R->R, f(x)=ax+b, stiind ca au loc relatiile f(-1)=-4 si (f o f)(-1)=-5

Answer 1

f(-1)=-4

-a+b=-4

b=a-4

(f o f)(-1)=-5

f(f(-1))=-5

f(-a+b)=-5

a(-a+b)+b=-5

-a²+ab+b=-5

Si inlocuim b=a-4:

-a²+a(a-4)+a-4=-5

-a²+a²-4a+a-4=-5

-3a=-5+4

-3a=-1

a=1/3

b=a-4=1/3-4=(1-12)/3=-11/3

f:R->R, f(x)=(x-11)/3