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Pertanyaan

Diketahui fungsi f : R → R , g : R → R , dan h : R → R dinyatakan oleh rumus f ( x ) = 3 x dan g ( x ) = x 2 + 3 , dan h ( x ) = 3 − x a. Tentukan nilai ( f ∘ g ∘ h ) ( 2 )

Diketahui fungsi  dan  dinyatakan oleh rumus  dan , dan  

a. Tentukan nilai  

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Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Jawaban

nilai dari adalah .

nilai dari begin mathsize 14px style open parentheses f ring operator g ring operator h close parentheses open parentheses 2 close parentheses end style adalah undefined.

Pembahasan

Diketahui fingsi , , dan . Selanjutnya, akan dicari - Nilai - Nilai - Nilai Dengan demikian, nilai dari adalah .

Diketahui fingsi begin mathsize 14px style f open parentheses x close parentheses equals 3 x end stylebegin mathsize 14px style g open parentheses x close parentheses equals x squared plus 3 end style, dan begin mathsize 14px style h open parentheses x close parentheses equals 3 minus x end style. Selanjutnya, akan dicari

- Nilai begin mathsize 14px style open parentheses g ring operator h close parentheses open parentheses x close parentheses end style 

begin mathsize 14px style open parentheses g ring operator h close parentheses open parentheses x close parentheses equals open parentheses g open parentheses h open parentheses x close parentheses close parentheses close parentheses space space space space space space space space space space space space space space equals g open parentheses 3 minus x close parentheses space space space space space space space space space space space space space space equals open parentheses 3 minus x close parentheses squared plus 3 space space space space space space space space space space space space space space equals 9 minus 6 x plus x squared plus 3 space space space space space space space space space space space space space space equals x squared minus 6 x plus 12 end style 

- Nilai begin mathsize 14px style open parentheses f ring operator left parenthesis g ring operator h right parenthesis close parentheses open parentheses x close parentheses end style 

size 14px left parenthesis size 14px f size 14px ring operator begin mathsize 14px style left parenthesis g ring operator h right parenthesis end style size 14px right parenthesis begin mathsize 14px style left parenthesis x right parenthesis end style size 14px equals size 14px f begin mathsize 14px style left parenthesis open parentheses g ring operator h close parentheses open parentheses x close parentheses right parenthesis end style size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px equals size 14px f begin mathsize 14px style left parenthesis x squared minus 6 x plus 12 right parenthesis end style size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px equals size 14px 3 begin mathsize 14px style left parenthesis x squared minus 6 x plus 12 right parenthesis end style size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px space size 14px equals size 14px 3 size 14px x to the power of size 14px 2 size 14px minus size 14px 18 size 14px x size 14px plus size 14px 36 

- Nilai begin mathsize 14px style open parentheses f ring operator g ring operator h close parentheses open parentheses 2 close parentheses end style

begin mathsize 14px style open parentheses f ring operator g ring operator h close parentheses open parentheses x close parentheses equals open parentheses f ring operator open parentheses g ring operator h close parentheses close parentheses open parentheses x close parentheses open parentheses f ring operator g ring operator h close parentheses open parentheses 2 close parentheses equals 3 x squared minus 18 x plus 36 open parentheses f ring operator g ring operator h close parentheses open parentheses 2 close parentheses equals 3 open parentheses 2 close parentheses squared minus 18 open parentheses 2 close parentheses plus 36 open parentheses f ring operator g ring operator h close parentheses open parentheses 2 close parentheses equals 3 open parentheses 4 close parentheses minus 36 plus 36 open parentheses f ring operator g ring operator h close parentheses open parentheses 2 close parentheses equals 12 end style 

Dengan demikian, nilai dari begin mathsize 14px style open parentheses f ring operator g ring operator h close parentheses open parentheses 2 close parentheses end style adalah undefined.

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