Question

Ma puteti ajuta la acest exercitiu? Multumesc

Answer 1

Răspuns:

x₁ = 1 ; x₂ = 3

m = -1 ; n = 3

Explicație pas cu pas:

f : R --> R ; f(x) = x²-2x

y = 2x-3  ; f(x) ∩ y <=> f(x) = y =>

x²-2x = 2x-3  => x²-4x+3 = 0 <=>

x²-3x-x+3 = 0 <=> x(x-3)-(x-3) = 0 =>

(x-3)(x-1) = 0 => x₁ = 1 ; x₂ = 3

x₁ = 1 => f(1) = 1-2 = -1 => A(1 ; -1)

x₂ = 3 => f(3) = 9-6 = 3 => B = (3 ; 3)

-------------------------

f(1) = 2 ; f(2) = 1 ; f : R --> R ; f(x) = mx+n

f(1) = m+n = 2

f(2) = 2m+n = 1

{m+n = 2

{2m+n = 1

=========

2m+n-m-n = 1-2 => m = -1 ; n = 3 =>

f(x) = -x+3