Question

A função f em R é tal que f(2x) = 3x + 1. Determine 2.f(3x + 1).

Answer 1

$f(2x)=3x+1\\f(2k)=3k+1$

Queremos fazer com que 2k = 3x + 1, logo:

$2k=3x+1~~~\therefore~~~\boxed{\boxed{k=\dfrac{3x+1}{2}}}$
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$f(2k)=3k+1$

Como 2k = 3x + 1 quando k = (3x + 1) / 2:

$f(3x+1)=3\left(\dfrac{3x+1}{2}\right)+1\\\\\\f(3x+1)=\dfrac{9x+3}{2}+1\\\\\\f(3x+1)=\dfrac{9x+3+2}{2}\\\\\\\boxed{\boxed{f(3x+1)=\dfrac{9x+5}{2}}}$

Logo, 2.f(3x + 1) será:

$2\cdot f(3x+1)=2\cdot\dfrac{9x+5}{2}\\\\\\\boxed{\boxed{2\cdot f(3x+1)=9x+5}}$