Question

Fie f:R->R , f(x)=2x-3 . Sa se rezolve ecuatiile:
a) f(x-1)=3+x
b)f(x+3)+2f(x-1)=f(1)

Answer 1

a)
f ( x - 1) = 3 + x
2 ( x - 1) - 3 = 3 + x 
2x - 2 - 3 = 3 + x ⇒ 2x - x = 3 + 3 + 2
⇒ x = 8

b)
f ( x + 3) + 2f ( x - 1 ) = f(1)
2 ( x + 3) - 3 + 2[ 2 ( x-1 ) - 3] = -1
2x + 6 - 3 + 2 ( 2x - 2 - 3) = -1
2x + 3 + 4x - 4 - 6 = -1
6x = -1 + 6 + 4 - 3 ⇒ 6x = 6 ⇒ x = 1