Question

Das funções f( x ) = - x - 3 e g( x ) = 4 k + k, determine o valor de k de modo que f o g = g o f.​

Answer 1

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$\sf f(x)=-x-3~~~g(x)=4x+k\\\sf f\circ g=f[g(x)]=-g(x)-3\\\sf f\circ g=-(4x+k)-3\\\sf f\circ g=-4x-k-3\\\sf g\circ f=g[f(x)]=4f(x)+k\\\sf g\circ f=4(-x-3)+k\\\sf g\circ f=-4x-12+k\\\sf f\circ g=g\circ f\\\sf-\diagdown\!\!\!\!\!4x-k-3=-\diagdown\!\!\!\!\!4x-12+k\\\sf k-12=-k-3\\\sf k+k=12-3\\\sf 2k=9\\\huge\boxed{\boxed{\boxed{\boxed{\sf k=\dfrac{9}{2}\checkmark}}}}$