Question

Fie functia f:R->R ; f(x)=ax+b. aflati a,b € R stiind ca f(1-x)+3f(x)=x+2

Answer 1

Răspuns:

Explicație pas cu pas:

f(x) = ax + b

f(1 - x) = a(1 - x) + b = a - ax + b

f(1-x) + 3f(x) = x + 2

a - ax + b + 3ax + 3b = x + 2

2ax + a + 4b = x + 2

2a = 1

a + 4b = 2

a = 1/2

4b = 2 - a = 2 - 1/2 = 3/2

b = 3/2 : 4 = 3/8

f(x) = ax + b = x/2 + 3/8