Question

Podaj dziedzinę f. Oblicz f(-3), f(1), f(3) a). f(x)= x kwadrat +21 dzielone przez x kwadrat -3 b). f(x)= 4x +2 dzielone przez x kwadrat -x-2

Answer 1

a)  f(x) = (x²+21)/(x²-3)                          D:    x²-3≠0

                                                                (x-√3)(x+√3) ≠ 0  ⇒ x-√3≠0 ∧ x+√3≠0

                                                                                            x≠√3   ∧ x≠ -√3

                                                                                 D= R\ {√3, -√3}

  f(-3)=[(-3)²+21]/[(-3)²-3]=(9+21)/(9-3)=30/6=5

  f(-1)= (1+21)/(1-3) = 22/-2 = -11

  f(3) = f(-3) = 5

b) f(x)= (4x+2)/(x²-x-2)                         D:  x²-x-2≠0

                                                                Δ=b²-4ac = 1+8=9,  √Δ=3

                                                             x₁= 2,  x₂= -1,   D= R\ {2, -1}

  f(-3) = [4·(-3)+2]/[(-3)²-(-3)-2] = (-12+2)/(9+3-2) = -10/10 = -1

  f(1) = (4·1+2)/(1²-1-2) = 6/-2 = -3

  f(3) = (4·3+2)/(3²-3-2) = (12+2)/(9-5) = 14/4 = 3½