Question

Dau coroana si 28 de puncte.
Materie clasa a 10 a.
Multumesc anticipat.​

Answer 1

Salutare!

f,g : R → R

f(x) = x² - 3x + 2

g(x) = 2x - 1

( f ° g )(x) = 0

( f ° g )(x) = ( 2x - 1 )² - 3 ( 2x - 1 ) + 2

( f ° g )(x) = 0 ⇒ ( 2x - 1 )² - 3 ( 2x - 1 ) + 2 = 0

4x² - 4x + 1 - 6x + 3 + 2 = 0

4x² - 10x + 6 = 0   | :2

2x² - 5x + 3 = 0

a = 2  ;  b = -5  ;  c = 3

Δ = b² - 4ac = (-5)² - 4 · 2 · 3 = 25 - 24 = 1

x₁,₂ = ( -b±√Δ ) / 2a = ( 5 ± 1 ) / 4

x₁ = ( 5 + 1 ) / 4 = 6 / 4 = 3 / 2

x₂ = ( 5 - 1 ) / 4 = 4 / 4 = 1

Solutii: x₁ = 3 / 2  ;  x₂ = 1

Answer 2

Răspuns:

Explicație pas cu pas:

f(x) = x^2 - 3x + 2

g(x) = 2x - 1

(fog)(x) = f(g(x))

(2x - 1)^2 - 3(2x - 1) + 2 = 0

4x^2 - 4x + 1 - 6x + 3 + 2 = 0

4x^2 -10x + 6 = 0

2x^2 - 5x + 3 = 0

Δ = 25 - 24 = 1

x1 = (5 + 1)/4 = 6/4 = 3/2

x2 = (5 - 1)/4 = 4/4 = 1