Răspuns:
f(x)=ax+b
a) f(2)=0 <=> 2a+b = 0
f(0)=4 <=> a*0+b = 4 => b = 4
2a+b = 0 => 2a+4=0 => 2a = -4 => a = -2
f(x)= -2x+4
Verificare: f(2)=0 => -2*2+4 = -4+4 = 0 (Adevarat)
f(0)=4 => -2*0+4 = 4 (Adevarat)
b) f(3a-1)=0 => a(3a-1)+b = 0 <=> [tex]3a^2-a+b[/tex] = 0
f(0)= -4 => a*0+b = -4 => b = -4
[tex]3a^2-a-b[/tex] = 0 <=> [tex]3a^2-a-4[/tex] = 0 <=> [tex]3a^2-a-4 <=> 3a^2+3a-4a-4 <=> 3a(a+1)-4(a+1) <=> (a+1)(3a-4)\\=> a1 = -1 ; a2 = 4/3[/tex]
f(x) = -x-4 ; f(x)= [tex]\frac{4x}{3}[/tex]-4
Verificare: f(0) = -4 => -0-4 = -4 (Adevarat)
f(0)= [tex]\frac{4*0}{3} - 4 = -4[/tex]
c) f(7+2a) = 0 <=> a(7+2a)+b = 0 <=> [tex]7a+2a^2+b = 0[/tex]
f(0)= -3a <=> a*0+b = -3a <=> b = -3a
[tex]7a+2a^2-3a = 0 <=> 2a^2+4a = 0 => 2a(a+2)=0 => \\=> a1 = 0 ; a2 = -2[/tex]
=> b = -3a <=> b1 = 0 ; b2 = 6
f(x)= 0*x+6 = 6 ; f(x)= -2x+6
Verificare: (cand a = b = 0) : f(0)=0 (adevarat)
cand a = -2; b = 6 => f(0)= 6 => -2*0+6 = 6 (Adevarat)
Explicație pas cu pas:
