Question

Quem tiver tempo e poder me ajudar
Determine as funções.

Answer 1

2 - 
A) 
     4.x² + 9 = 12.x                     12 +-√0  ------> x1 = 12/ 8 => 3/2
     4.x² - 12.x + 9 = 0                 2.4       -------> x2 = 12/8 => 3/2
     Δ  = (-12)² - 4.4.9 => 0

 Xv = -b/2.a => 12/2.4 => 3/2
 Yv = -Δ/4.a => -0/4.4 => 0

Im(f(x)) = {3/2, 0 }
D(f(x)) = {x∈R/ x = 3/2}

B)  x² = x +12                     1+-√49 -----> x1 = 1+7/2 => 4
     x²-x-12 = 0                     2.1  ---------> x2 = 1-7/2 => -3
     Δ = 1² - 4.1.-12 => 49
   
Xv = -b/2.a => 1/2.1 => 1/2
Yv = -Δ/4.a => -49/4.1 => -49/4

Im(f(x)) = {-3,1/2,4,-49/4}
D(f(x)) = {x ∈ IR/  -3 > x < 4}

C)         2.x² = -12.x-18                     -12+-0 ---------> x1 = -12/4 = -3
            2.x² + 12.x + 18 = 0               2.2     -------> x2 = -12/4 = -3
            Δ = 12² -4.2.18 => 0

Xv= -b/2.a = -12/2.2 => -3
Yv = -Δ/4.a = -0/4.2 => 0

Im(f(x)) = {-3,0}
D(f(x)) =  { x∈ R/ x = -3 }

D) x² +9= 4.x
    x² -4.x + 9 = 0
    Δ = (-4)² - 4.1.9 => -20

Im(f(x))= ⊅ IR
D(f(x)) = ⊅ IR

E) 25.x² = 20.x-4                         20+-0 --------------- x1 = x2 = 2/5
    25.x² - 20.x + 4 = 0                 2.25
    Δ = (-20)² - 4.25.4 => 0

Xv = -b/2.a = 20/2.25 => 2/5
Yv = -Δ/4.a => 0

Im(f(x)) = {2/5,0}
Dm(f(x)) = {x ∈ R/ x = 2/5}

F) 2.x = 15-x²                   -2+-√64 ----------> x1 = -2+8/2 => 3
    x²+2.x - 15 = 0              2.1         ----------> x2 = -2 - 8/2 => -5
   Δ = 4-4.1-15 => 64
 
Xv= -b/2.a => -2/2.1 => -1
Yv = -Δ/4.a => -64/4.1 => -16

Im(f(x)) = {-16,-5,-1,3}
D(f(x)) = { x ∈ R/ -5 < x < 3}

G) x²+3.x-6 = -8                -3+-√1 ---------> x1 =  -1
     x² + 3.x +2 = 0               2.1   --------> x2 = -2
     Δ = 3² - 4.1.2 => 1

Xv = -b/2.a => -3/2.1 => -3/2
Yv = -Δ/4.a => -1/4.1 => -1/4

H) x²+x-7 = 5                   -1 +- √49 --------------> x1 = -1-7/2 => -4
    x²+x-12 = 0                    2.1     ------------------> x2 = -1+7/2 => 3
    Δ = 1² - 4.-12 => 49

Xv = -b/2.a => -1/2.1 => -1/2
Yv = -Δ/4.a => -49/4.1 => -49/4

Im(f(x)) = {-49/4,-4,-1/2,3}
D(f(x)) = } x ∈ R/ -4< x < 3 }