Question

13 - (INFO)

Dadas as funções f(x) = 4x + 5 e g(x) = 2x - 5k, ocorrerá gof(x) = fog(x) se e somente

se k for igual a:

a) -1/3

b) 1/3

c) 0

d) 1

e) -1

Answer 1

$f(x)=4x+5\\g(x)=2x-5k$
_________

Achando gof(x):

$gof(x)=g(f(x)\\\\gof(x)=2f(x)-5k\\\\gof(x)=2(4x+5)-5k\\\\gof(x)=8x+10-5k$
_________

Achando fog(x):

$fog(x)=f(g(x))\\\\fog(x)=4g(x)+5\\\\fog(x)=4(2x-5k)+5\\\\fog(x)=8x-20k+5$
_________

Fazendo gof(x) = fog(x):

$8x+10-5k=8x-20k+5\\\\10-5k=-20k+5\\\\-5k+20k=5-10\\\\15k=-5\\\\k=-5/15\\\\\boxed{\boxed{k=-\dfrac{1}{3}}}$

Letra A