Question

Considere uma função afim f(x) tal que:
f(1) = 12
f(2) = 19
Determine o valor de x tal que:
f(2x + 1) + 2.f(3x − 2) = f( x -7)

A)0
B)-1
C)-3/25
D)-38/49
E)-43/64

Answer 1

Olá!

f(1)= a*(1) +b

12= a+b

f(2)= a * (2) +b

19= 2a +b

a+b= 12

2a +b= 19

-a= -7

a= 7

a+b= 12

7 + b= 12

b= 12-7

b= 5

f(x)= 7x + 5

f(2x+1)= 7*(2x+1) +5

f(2x+1)= 14x +7 +5

f(2x+1)= 14x +12

f(3x-2) = 7* (3x-2) +5

f(3x-2)= 21x -14 +5

f(3x-2)= 21x - 9

2 f(3x-2)= 2 *(21x-9)

2 f(3x-2)= 42x - 18

f(x-7) = 7* (x- 7) +5

f(x-7)= 7x -49 +5

f(x-7)= 7x - 44

f(2x+1) + 2 * f(3x-2) = f(x-7)

14x +12 + 42x -18= 7x -44

14x +42x -7x= -44 -12 +18

49x= -38

x= -38/49

Resposta: Letra d) -38/49

Bons estudos!

T.H.S.