Question

Seja a função afim f: ℝ → ℝ tal que f(3x + 1) = 2x – 3. Escreva a função f(x).

Answer 1

Resposta:

f(x)=2x/3-11/3

Explicação passo-a-passo:

f(x)=ax+b

f(3x+1)=a(3x+1)+b

f(3x+1)=3ax+a+b

a=2/3

f(3x+1)=3.2/3.x+2/3+b

f(3x+1)=2x+2/3+b

2/3+b=-3

b=-3-2/3

b=(-9-2)/3

b=-11/3

f(x)=2x/3-11/3

f(3x+1)=2(3x+1)/3-11/3

f(3x+1)=6x/3+2/3-11/3

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