Question

Sejam f e g funções reais tal que f(x) = 2x – 5 e g(x) = 3 – 4x. DETERMINE: a) f(g(x)) b) g ο f (–3) ( c) f(g(f(2)))

Answer 1

Explicação passo-a-passo:

a) $\sf f(g(x))=f(3-4x)$

$\sf f(g(x))=2\cdot(3-4x)-5$

$\sf f(g(x))=6-8x-5$

$\sf f(g(x))=1-8x$

b) $\sf f(x)=2x-5$

• $\sf f(-3)=2\cdot(-3)-5$

$\sf f(-3)=-6-5$

$\sf f(-3)=-11$

Assim, $\sf g(f(-3)=g(-11)$

• $\sf g(x)=3-4x$

$\sf g(-11)=3-4\cdot(-11)$

$\sf g(-11)=3+44$

$\sf g(-11)=47$

Logo, $\sf g(f(-3))=47$

c) $\sf f(g(f(2)))$

• $\sf f(2)=2\cdot2-5$

$\sf f(2)=4-5$

$\sf f(2)=-1$

Assim, $\sf f(g(f(2)))=f(g(-1))$

• $\sf g(-1)=3-4\cdot(-1)$

$\sf g(-1)=3+4$

$\sf g(-1)=7$

Desse modo, $\sf f(g(f(2)))=f(7)$

• $\sf f(7)=2\cdot7-5$

$\sf f(7)=14-5$

$\sf f(7)=9$

Logo, $\sf f(g(f(2)))=9$