Question

f(x)=x-1;g(x)=3-2x;h(x)=x^2+3x,
a)(f-3g)(x)mai mic sau egal cu 0.
b)h(-x)=4.
c)(g compus 2f)(x)-(h compus f)(-x).
Va rog frumos!

Answer 1

Răspuns:

Explicație pas cu pas:

f(x)=x-1

g(x)=3-2x

h(x)=x^2+3x=x(x+3)

a) (f-3g)(x)<=0

x-1-3(3-2x)<=0=>x-1-9+6x<=0=>7x-10<=0=>x€(-inf, 10/7]

b) h(-x)=4=>x^2-3x-4=0=>x^2-1-3x-3=0=>(x-1)(x+1)-3(x+1)=0=>(x+1)(x-1-3)=0=>(x+1)(x-4)=0=>x=-1 și x=4

c)(g compus 2f)(x)-(h compus f)(-x)=7-4x-x^2+x+3=-x^2-3x+10=0=>-(x^2+3x-10)=0=>-(x^2-4+3x-6)=0/*(-1)=>(x-2)(x+2)+3(x-2)=0=>(x-2)(x+2+3)=0=>x=2 și x=-5

(g•2f)=3-4f(x)=3-4(x-1)=3-4x+4=7-4x

(h•f)(-x)=f(-x)^2+3f(-x)=(-x-1)^2+3(-x-1)=x^2+2x+1-1-3x-3=x^2-x-3