Question

Cât de repede posibil vă rog:))​

Answer 1

Răspuns:

Explicație pas cu pas:

f(x) = { 4x ; x ∈ (-∞ ; 1]

        { 2 ; x ∈ (1 ; 3)

        { 2x - x² ; x ∈ [3 ; +∞)

f : R --> R

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a) x = 4 => f(4) = 2·4-4² = 8-16 = -6

   x = 5/2 => f(5/2) = 2

f(-4) = 4·(-4) = -16

f(18/5) = ⁵⁾2·18/5 - (18/5)² = -144/25

f(-21/4) = 4·(-21/4) = -21

f(-6,75) = 4·(-6,75) = -27

f(5) = 2·5 - 5² = -15

f(2 1/5) = f(11/5) = 2

f(45/43) = 2

f(0,16) = 4·0,16 = 0,64

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b) f(x) = -3 => {4x = -3 => x = -3/4

                     {2x-x² = -3 => x²-2x-3 = 0 => x₁,₂ = (2±√(4+12)/2 =>

                      x₁,₂ = 1±2 => x₁ = -1 nu convine ; x₂ = 3

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f(x) = 3/2 => {4x = 3/2 => x = 3/8

                   {2x-x² = 3/2 => 2x²-4x+3 = 0 => x₁,₂ = (4±√(16-24)/4 ∉ R

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f(x) = 2 => {x ∈ (1 , 3)

                {4x = 2 => x = 1/2

                {2x-x² = 2 => x²-2x+2 = 0 => x₁,₂ = (2±√(4-8)/4 ∉ R

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f(x) = 0 => {4x = 0 => x = 0

                {2x-x² = 0 => x(2-x) = 0 => x = 0 ; x = 2 , nu convine

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f(x) = -15 => {4x = -15 => x = -15/4

                   {2x-x² = -15/4 => 4x²-8x-15 = 0 =>

                  x₁,₂ = (8±√(64+240)/8 = (8±4√19)/8 = (2±√19)/2 =>

                 x = (2+√19)/2

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f(x) = 1 => {4x = 1 => x = 1/4

               {2x-x² = 1 => x²-2x+1 = 0 => x₁,₂ = 1 , nu convine

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f(x) = 2 1/4 = > f(x) = 9/4 => {4x = 9/4 => x = 9/16

                                           {2x-x²=9/4 =>4x²-8x+9 = 0 => x ∉ R