Question

Se da fuctia g:R-R
g(x)=-2x
a)Sa se determine imaginea prin g a multimilor [-2;5],(-1/2;1/2),(-3/2;+infinit),(-infinit;5/2],{-6.10}.
b)Sa sedetermine preimaginea prin g a multimilor (-infinit;4],(-2;+infinit),[-6;2],[-2/3;6),(-1/4,1/2)

Answer 1

a)
-2<= x<= 5     => -4>= -2x >= -10 => img=[-10;-4]
-1< x<=-1/2     => -2>= -2x >= -1 => img=[-2;-1)
-3/2<= x     => 3>= -2x => img=[3;+infinit)
 5/2<=x     => -5>= -2x => img=[-infinit;-5)
-6.10=x     => 12.20= -2x => img={12.20}
b)
 -2x<=4   => x>=-2
 -2x>-2  => x<1
-6<=-2x<=2 => 2>=x>=-1
-2/3<=-2x<6 => 1/3>=x>-3
-1/4<-2x<1/2 => 1/8>=x>=-1/4