Pertanyaan

f ( x ) = 2 x 2 − 1 ; nilai f ( 1 ) = ...

$f (x) = 2 x^{2} - 1; nilai f (1) = ...$

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Jawaban terverifikasi

Jawaban

nilai

f apostrophe left parenthesis 1 right parenthesis equals 2

Pembahasan

Ingat jika Diketahui Sehingga diperoleh Nilai Jadi, nilai

Ingat jika

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell U to the power of n end cell row cell f apostrophe open parentheses x close parentheses end cell equals cell n times U to the power of n minus 1 end exponent times U apostrophe end cell end table

Diketahui

Sehingga diperoleh

$table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe open parentheses x close parentheses end cell equals cell n times U to the power of n minus 1 end exponent times U apostrophe end cell row blank equals cell 1 half times open parentheses 2 x squared minus 1 close parentheses to the power of 1 half minus 1 end exponent times 4 x end cell row blank equals cell 2 x times open parentheses 2 x squared minus 1 close parentheses to the power of negative 1 half end exponent end cell row blank equals cell fraction numerator 2 x over denominator open parentheses 2 x squared minus 1 close parentheses to the power of begin display style 1 half end style end exponent end fraction end cell row blank equals cell fraction numerator 2 x over denominator square root of open parentheses 2 x squared minus 1 close parentheses end root end fraction end cell end table$

Nilai f apostrophe left parenthesis 1 right parenthesis

$table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe left parenthesis x right parenthesis end cell equals cell fraction numerator 2 x over denominator square root of left parenthesis 2 x squared minus 1 end root end fraction end cell row cell f apostrophe left parenthesis 1 right parenthesis end cell equals cell fraction numerator 2 left parenthesis 1 right parenthesis over denominator square root of 2 left parenthesis 1 right parenthesis squared minus 1 end root end fraction end cell row blank equals cell fraction numerator 2 over denominator square root of 2 minus 1 end root end fraction end cell row blank equals 2 end table$

Jadi, nilai f apostrophe left parenthesis 1 right parenthesis equals 2