Matematica - Ecuatii si inecuatii. Functii

Ecuatii si inecuatii. Functii - Intrebarea 24

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Fie funcţia $f colon straight real numbers rightwards arrow straight real numbers comma space f left parenthesis x right parenthesis equals open parentheses m minus 1 close parentheses x squared plus open parentheses m plus 2 close parentheses x plus m plus 1 comma space m element of straight real numbers backslash open curly brackets 1 close curly brackets.$ Să se determine valorile parametrului real $m$ astfel încât $f left parenthesis x right parenthesis less or equal than 0 comma space open parentheses for all close parentheses x element of straight real numbers$ .

m element of open parentheses negative infinity comma 1 close parentheses

m element of left parenthesis negative infinity comma fraction numerator 2 minus 2 square root of 7 over denominator 3 end fraction right square bracket

m element of left parenthesis negative infinity comma fraction numerator 2 plus 2 square root of 7 over denominator 3 end fraction right square bracket

Raspunsul este corect.

Raspunsul este gresit.

Explicatie:

Răspuns corect: B

$f left parenthesis x right parenthesis less or equal than 0 comma space open parentheses for all close parentheses x element of straight real numbers left right double arrow open curly brackets table attributes columnalign left end attributes row cell increment greater or equal than 0 end cell row cell m minus 1 less than 0 end cell end table close left right double arrow open curly brackets table attributes columnalign left end attributes row cell open parentheses m plus 2 close parentheses squared minus 4 open parentheses m squared minus 1 close parentheses greater or equal than 0 end cell row cell m minus 1 less than 0 end cell end table close left right double arrow open curly brackets table attributes columnalign left end attributes row cell m element of left parenthesis negative infinity comma fraction numerator 2 minus 2 square root of 7 over denominator 3 end fraction right square bracket union left square bracket fraction numerator 2 plus 2 square root of 7 over denominator 3 end fraction comma plus infinity right parenthesis end cell row cell m element of open parentheses negative infinity comma 1 close parentheses end cell end table close left right double arrow m element of left parenthesis negative infinity comma fraction numerator 2 minus 2 square root of 7 over denominator 3 end fraction right square bracket$