Question

Determine K sabendo que:
g(x)= 3x - K
f(x)=4x - 1
e (gof) (x) = 12x - 15

Answer 1

(gof)(x)=12x-15

g(f(x))=12x-15

g(4x-1)=12x-15
3(4x-1)-K=12x-15
12x-3-K=12x-15 cortando 12x temos
-3-K=-15 então K=12.

Answer 2

Se $g(x)=3x-k\,,$ então

$(g \circ f)(x)=g[f(x)]\\\\ (g \circ f)(x)=3\,f(x)-k$


Substituindo o lado esquerdo pelo que foi dado no enunciado, temos,

$12x-15=3\,f(x)-k\\\\ 12x-15=3\,(4x-1)-k\\\\ 12x-15=12x-3-k\\\\ k=12x-3-12x+15\\\\\ k=-3+15\\\\\ \boxed{\begin{array}{c} k=12 \end{array}}$