Question

as funções F e G são dados por F(x)=3/5 x-1 e G(x)= 4/3 x+a. sabe-se que F(0)= - G(0)=1/3. O 
valor de F(3) - 3G (1/5) é?  deixe claro a resposta agradeço.

Answer 1

→ calculamos o f(0)

f(0) = 3/5x - 1
f(0) = 3/5.0 - 1
f(0) = 0 - 1
f(0) = -1

→ agora o g(0)

g(0) = 4/3x + a
g(0) = 4/3.0 + a
f(0) = 0 + a 
f(0) = a

→ agora calculamos o valor de a :

f(0) - g(0) = 1/3
-1 - a = 1/3
-a = 1/3 + 1
-a = 4/3
a = -4/3

→ agora calculamos o valor de f(3) 

f(3) = 3/5x - 1
f(3) = 3/5.3 - 1
f(3) = 9/5 - 1
f(3) = 4/5

→ agora o g(1/5)

g(1/5) = 4/3x + a
g(1/5) = 4/3.1/5 + (-4/3)
g(1/5) = 4/15 + (-4/3)
g(1/5) = -16/15

→ agora calculamos 3g(1/5)

3.(-16/15) = -16/5

→ Por fim , fazemos f(3) - 3g(1/5)

4/5 - (-16/5) = 20 / 5 = 4

Answer 2

Siga os passos:

$f(0)= \frac{3}{5} *0-1\\\\\boxed{f(0)=-1}\\\\\\g(0)= \frac{4}{3}*0+a\\\\\boxed{g(0)=a}\\\\\\f(0)-g(0)= \frac{1}{3} \\\\-1-a= \frac{1}{3} \\\\\boxed{a=- \frac{4}{3}}$

$f(3)= \frac{3}{5}*3-1\\\\f(3)= \frac{9}{5} -1\\\\\boxed{f(3)= \frac{4}{5}}\\\\\\g( \frac{1}{5} )= \frac{4}{3}* \frac{1}{5}+(- \frac{4}{3} )\\\\g( \frac{1}{5} )= \frac{4}{15}- \frac{4}{3} \\\\g( \frac{1}{5} )= \frac{4-20}{15} \\\\\boxed{g( \frac{1}{5} )=- \frac{16}{15}}$


$f(3)-3*g( \frac{1}{5} )=\\\\\Rightarrow~~ \frac{4}{5}-3*(- \frac{16}{15} )\\\\\Rightarrow~~ \frac{4}{5} + \frac{48}{15} \\\\\Rightarrow~~ \frac{12+48}{15} \\\\\Rightarrow~~ \frac{60}{15} =4\\\\\\\boxed{\boxed{Resposta:~~4}}$