Question

Dadas as funções reais f(x) = 2x – 6 e g(x) = mx + n, se f[g(x)] = 12x + 8, qual o valor de m - n ?

Answer 1

$f^{\circ}g(x)=f[g(x)]=2.g(x) -6\\f^{\circ}g(x)=2(mx+n)-6\\f^{\circ}g(x)=2mx+2n-6$

$12x+8=2mx+2n-6$

$2m\cancel{x} =12\cancel{x}\\m=\dfrac{12}{2}=6$

$2n-6=8\\2n=6+8\\2n=14\\n=\dfrac{14}{2}=7$

$\boxed{\boxed{\mathsf{m-n=6-7=-1}}}$