alguém pode me ajudar??
Soluções para a tarefa
Resposta:
As funções f e g são dadas por fx=3/5x-1 e gx=4/3x+a.
Achar o VALOR de (a)
Sabe-se que f(0)-g(0)=1/3.
f(0) - g(0) = 1/3
f(x) = 3/5x - 1
f(0) = 3/5(0) - 1
f(0) = 0/5 - 1
f(0) = 0 - 1
f(0) = - 1
e
g(x) = 4/3x + a
g(0) = 4/3(0) + a
g(0) = 0/3 + a
g(0) = 0 + a
g(0) = a
SE
f(0) = - 1
g(0) = a
f(0) - g(0) = 1/3
-1 - a = 1/3
-a = 1/3 + 1
1(1) + 3(1)
-a = --------------
3
1 + 3
-a = --------
3
-a = 4/3
a = - 4/3
ficando ASSIM
g(x) = 4/3x + a
g(x) = 4/3x - 4/3
Determine f(3)-3g(1/5) ?
f(x) = 3/5x - 1
f(3) = 3/5(3) - 1
f(3) = 3(3)/5 - 1
f(3) = 9/5 - 1
9
f(3) = ---- - 1
5
1(9) -5(1)
f(3) = -----------
5
9 - 5
f(3) = --------
5
f(3) = 4/5
e
g(x) = 4/3x - 4/3
3g(1/5) = 4/3(1/5) - 4/3
4 (1) 4
3g(1/5) = ---------- - -----
3(5) 3
4 4
3g(1/5) = --------- - -------
15 3 mmc 15, 3 = 15
1(4) - 5(4)
3g(1/5) = --------------
15
4 - 20
3g(1/5) = ---------
15
16
3g(1/5) = - --------
15
3g(1/5) = 3(-16/15)
3g(1/5) = - 48/15
DETERMINE
f(3) = 4/5
3g(1/5) = -48/15
f(3) - 3g(1/5) =
4/5 - (-48/15)
4/5 + 48/15 mmc 5,15 = 15
4 48
---- + ------
5 15
3(4) + 1(48)
----------------
15
12 + 48 60
---------- = ------- = 4
15 15