Question

Sendo f(x-1) = 2x+4, encontre f(x). Explicada, por favor.​

Answer 1

Resposta:

f(x)=2x+6

Explicação passo-a-passo:

Sabendo que : f(x)=ax+b

f(x-1)=2x+4

Substituindo (x-1) na função f(x)=ax+b :

a.(x-1)+b=2x+4

ax-a+b=2x+4

a=2

-a+b=4 b=4+a=4+2= 6

F(x)=ax+b

F(x)=2x+6

Answer 2

Resposta:

$\boxed{\mathtt{2x + 6}}$

Explicação passo-a-passo:

$\\ \displaystyle \mathsf{f(x - 1) = 2x + 4} \\\\ \mathsf{f(x - 1) = 2 \cdot (x + 2)} \\\\ \mathsf{f(x - 1) = (x + 2) + (x + 2)} \\\\ \mathsf{f(x - 1) - 1 - 1 = (x + 2 + x + 2) - 1 - 1} \\\\ \mathsf{f(x - 1) - 2 = (x - 1 + x - 1) + 2 + 2} \\\\ \mathsf{f(x - 1) - 2 = (x - 1) + (x - 1) + 4} \\\\ \mathsf{f(x - 1) = 2 \cdot (x - 1) + 4 + 2} \\\\ \mathsf{f(x - 1) = 2(x - 1) + 6} \\\\ \boxed{\boxed{\mathsf{f(x) = 2x + 6}}}$