Question

sendo f(2x-1)=6x-1, calcule f(x)

Answer 1

f(2x-1)= 6.(2x-1)-1 logo 12x-6-1
f(2x-1)= 12x-7 = x= 7/12

Answer 2

Seja

$u(x) = 2x - 1$

Temos que

$f(2x - 1) = f(u(x)) = 6x - 1$

Como

$u(x) = 2x - 1$

então

$2x - 1 = u(x) \\ 2x = u(x) + 1 \\ x = \frac{u(x) + 1}{2}$

Daí,

$f(u(x)) = 6 \times ( \frac{u(x) + 1}{2} ) - 1 \\ f(u(x)) = \frac{6u(x) + 6}{2} - \frac{2}{2} \\ f(u(x)) = \frac{6u(x) + 6 - 2}{2} \\ f(u(x)) = \frac{6u(x) + 4}{2} \\ f(u(x)) = 3u(x) + 2$


Logo,

$f(x) = 3x + 2$