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Diketahui fungsi  dengan  dan . Tentukan rumus fungsi .

Pertanyaan

Diketahui fungsi begin mathsize 14px style f left parenthesis x right parenthesis end style dengan begin mathsize 14px style f apostrophe left parenthesis x right parenthesis equals 3 left parenthesis 4 x cubed plus x squared minus 2 x right parenthesis end style dan size 14px f size 14px left parenthesis size 14px minus size 14px 1 size 14px right parenthesis size 14px equals size 14px minus size 14px 11. Tentukan rumus fungsi undefined.

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Pembahasan Video:

Pembahasan Soal:

Diketahui begin mathsize 14px style f apostrophe left parenthesis x right parenthesis equals 3 left parenthesis 4 x cubed plus x squared minus 2 x right parenthesis end style, maka fungsi begin mathsize 14px style f left parenthesis x right parenthesis end style dapat dicari dengan cara sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell integral f apostrophe left parenthesis x right parenthesis space d x end cell row blank equals cell integral 3 open parentheses 4 x cubed plus x squared minus 2 x close parentheses space straight d x end cell row blank equals cell 3 integral open parentheses 4 x cubed plus x squared minus 2 x close parentheses space d x end cell row blank equals cell 3 open parentheses x to the power of 4 plus 1 third x cubed minus x squared plus C close parentheses end cell row blank equals cell 3 x to the power of 4 plus x cubed minus 3 x squared plus C end cell end table end style

Diketahui size 14px f size 14px left parenthesis size 14px minus size 14px 1 size 14px right parenthesis size 14px equals size 14px minus size 14px 11, maka nilai begin mathsize 14px style C end style dapat ditentukan dengan cara sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis negative 1 right parenthesis end cell equals cell negative 11 end cell row cell 3 left parenthesis negative 1 right parenthesis to the power of 4 plus left parenthesis negative 1 right parenthesis cubed minus 3 left parenthesis negative 1 right parenthesis squared plus C end cell equals cell negative 11 end cell row cell 3 minus 1 minus 3 plus C end cell equals cell negative 11 end cell row cell negative 1 plus C end cell equals cell negative 11 end cell row C equals cell negative 10 end cell end table end style

Jadi, rumus fungsi undefined adalah begin mathsize 14px style f left parenthesis x right parenthesis equals 3 x to the power of 4 plus x cubed minus 3 x squared minus 10 end style.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 12 April 2021

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