Question

Determinați dacă este corect definită funcția:
a.)f:Z->N,f(x)=2x la puterea 2-1;
b.)f:N->Q,f(x)=2/3x+4;
c.)f:R->R,f(x)=-5/x;
d.)f:N->Z,f(x)=1/2x-3.

Answer 1

 

  OPTIMIZARE:

 

$\displaystyle\bf\\a)\\f:Z\to N,~f(x)=2x^2-1\\GRESIT~deoarece~f(0)=-1\notin N\\Corect~ar~fi:~~~f:Z\to N^*\\\\b)\\F:N\to Q,~f(x)=\frac{2}{3}x+4\\CORECT\\Chiar~daca~x~este~multiplu~de~3~si~rezulta~numar~natural,~este~corect\\deoarece~N\subset Q$

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$\displaystyle\bf\\c)\\F:R\to R,~f(x)=-\frac{5}{x}\\GRESIT~deoarece~x\neq 0\\Corect~ar~fi:~~~F:R^*\to R\\\\d)\\f:N\to Z,~f(x)=\frac{1}{2x-3}\\GRESIT\\D_1=\{-1;~1\}\\2x-3=-1~~\implies~2x=3-1\implies x=\frac{2}{2}={1}\\2x-3=1~~\implies~2x=3+1\implies x=\frac{4}{2}={2}\\Corect~ar~fi:~~~f:\{1;~2\}\subset N\to Z$