Question

1) Aratati ca f:R->R , f(x)= $\frac{1}{ x^{2} +2}$  nu este injectiva .
2) Rezolvati inecuatia : 2*$4^{x}$-3*$2^{x}$+1≥0

Answer 1

[tex]2*4^x-3*2^x+1 \geq 0 2*(2^2^)^x-3*2^x+1=0 2^x=t 2t^2-3t+1=0 a=2 b=-3 c=1 delta=b^2-4ac=(-3)^2-4*2*1=9-8=1 t1=3+1/4=4/4=1 t2=3-1/4=2/4=1/2 [/tex]

Revenim la substitutia $2^x=t$
[tex]2^x=1 =\ \textgreater \ x=0 2^x=1/2 x=log_21-log_22=0-1=-1 [/tex]


De unde rezulta ca x apartine(-infinit -1) (0 infinit)