Question

Dada a função f(x) = x/x+1 - 1/2x-3 calcule:

a) f ( 1 )

b) x de modo que f ( x )= 1/3

Answer 1

Dada a função
f(x) = x/(x+1) - 1/(2x-3) calcule:

a) f ( 1 )
f(1) = 1/(1+1) - 1/(2.1 - 3)
f(1) = 1/2 - 1/(2 - 3)
f(1) = 1/2 - 1/(-1)
f(1) = 1/2 + 1
f(1) = (1+2)/2
f(1) = 3/2

b) x de modo que f ( x ) = 1/3

f(x) = x/(x+1) - 1/(2x-3)
1/3 = x/(x+1) - 1/(2x - 3)
MMC = 3.(x + 1).(2x - 3)
(x+1).(2x-3) = 3.x.(2x-3) - 1.3.(x + 1)
2x^2 - 3x +2x -3 = 6x^2-9x-3x - 3
2x^2 - x - 3 = 6x^2 - 12x - 3
2x^2 - x = 6x^2 - 12x
0 = 6x^2 - 2x^2 - 12x + x
0 = 4x^2 - 11x
4x^2 - 11x = 0
x.(4x - 11) = 0
x = 0
4x - 11 = 0
4x = 11
x = 11/4

R.:
x = 0 ; x = 11/4