I.   f(x)⋅g(x) II.  f(g(x))  III. g(f(x)) Jika. f(x)=x3 dan g(x)=x2+1, manakah yang merupakan fungsi ganjil?

Pertanyaan

I.   f open parentheses x close parentheses times g open parentheses x close parentheses

II.  f open parentheses g open parentheses x close parentheses close parentheses 

III. g open parentheses f open parentheses x close parentheses close parentheses

Jika. f open parentheses x close parentheses equals x cubed dan g left parenthesis x right parenthesis equals x squared plus 1, manakah yang merupakan fungsi ganjil?

  1. Hanya Ispace

  2. Hanya IIspace

  3. Hanya IIIspace

  4. Hanya II dan IIIspace

  5. I, II dan III space

M. Nasrullah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B

Pembahasan

Ingat bahwa suatu fungsi dikatakan fungsi ganjil jika f open parentheses negative x close parentheses equals negative f open parentheses x close parentheses. Mari kita periksa satu-persatu pernyataan pada soa:

 

I.   f open parentheses x close parentheses times g open parentheses x close parentheses

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses times g open parentheses x close parentheses end cell equals cell open parentheses x cubed close parentheses open parentheses x squared plus 1 close parentheses end cell row blank equals cell x to the power of 5 plus x cubed end cell end table

Sehingga, fungsi f open parentheses x close parentheses times g open parentheses x close parentheses merupakan fungsi ganjil, karena table attributes columnalign right center left columnspacing 0px end attributes row cell negative open parentheses f open parentheses x close parentheses times g open parentheses x close parentheses close parentheses end cell equals cell f open parentheses negative x close parentheses times g open parentheses negative x close parentheses equals negative x to the power of 5 minus x cubed end cell end table

II.  f open parentheses g open parentheses x close parentheses close parentheses

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses g open parentheses x close parentheses close parentheses end cell equals cell f open parentheses x squared minus y squared close parentheses end cell row blank equals cell open parentheses x squared minus y squared close parentheses cubed end cell row blank equals cell x to the power of 6 plus 3 x to the power of 4 plus 3 x squared plus 1 end cell end table

Sehingga, fungsi f open parentheses g open parentheses x close parentheses close parentheses bukan merupakan fungsi ganjil, karena

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses g open parentheses negative x close parentheses close parentheses end cell not equal to cell negative open parentheses f open parentheses g open parentheses x close parentheses close parentheses close parentheses end cell row cell open parentheses negative x close parentheses to the power of 6 plus 3 open parentheses negative x close parentheses to the power of 4 plus 3 open parentheses negative x close parentheses squared plus 1 end cell not equal to cell negative open parentheses x to the power of 6 plus 3 x to the power of 4 plus 3 x squared plus 1 close parentheses end cell row cell x to the power of 6 plus 3 x to the power of 4 plus 3 x squared plus 1 end cell not equal to cell negative x to the power of 6 minus 3 x to the power of 4 minus 3 x squared minus 1 end cell end table

III. g open parentheses f open parentheses x close parentheses close parentheses

table attributes columnalign right center left columnspacing 0px end attributes row cell g open parentheses f open parentheses x close parentheses close parentheses end cell equals cell g open parentheses x cubed close parentheses end cell row blank equals cell open parentheses x cubed close parentheses squared plus 1 end cell row blank equals cell x to the power of 5 plus 1 end cell end table

Sehingga, fungsi g open parentheses f open parentheses x close parentheses close parentheses bukan merupakan fungsi ganjil, karena

table attributes columnalign right center left columnspacing 0px end attributes row cell g open parentheses f open parentheses negative x close parentheses close parentheses end cell not equal to cell negative open parentheses g open parentheses f open parentheses x close parentheses close parentheses close parentheses end cell row cell open parentheses negative x close parentheses to the power of 5 plus 1 end cell not equal to cell negative open parentheses x to the power of 5 plus 1 close parentheses end cell row cell negative x to the power of 5 plus 1 end cell not equal to cell negative x to the power of 5 minus 1 end cell end table

Jadi, jawaban yang tepat adalah B

148

5.0 (3 rating)

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