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Jika g ( x ) = ( x + 1 ) 2 dan ( g ∘ f ) ( x ) = ( lo g ( x ) ) 2 + 2 lo g ( x ) + 1 , nilai f ( 0 , 0001 ) = ....

Jika  dan , nilai ....

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F. Ayudhita

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

jawaban yang tepat adalah D.

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Pembahasan

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Masukan ke , sehingga: Ingat : ( Sifat Logaritma ) Jadi, jawaban yang tepat adalah D.

begin mathsize 14px style left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis equals left parenthesis log open parentheses x close parentheses right parenthesis squared plus 2 log open parentheses x close parentheses plus 1 g open parentheses f open parentheses x close parentheses close parentheses equals left parenthesis log open parentheses x close parentheses right parenthesis squared plus 2 log open parentheses x close parentheses plus 1 end style

Masukan begin mathsize 14px style f left parenthesis x right parenthesis end style ke begin mathsize 14px style g left parenthesis x right parenthesis equals left parenthesis x plus 1 right parenthesis squared end style, sehingga:

begin mathsize 14px style open parentheses f left parenthesis x right parenthesis plus 1 close parentheses squared equals left parenthesis log open parentheses x close parentheses right parenthesis squared plus 2 log open parentheses x close parentheses plus 1 end style

Ingat : begin mathsize 14px style left parenthesis a plus b right parenthesis squared equals a squared plus 2 a b plus b squared end style

size 14px left parenthesis size 14px f begin mathsize 14px style left parenthesis x right parenthesis end style size 14px plus size 14px 1 size 14px right parenthesis to the power of size 14px 2 size 14px equals begin mathsize 14px style left parenthesis l o g open parentheses x close parentheses plus 1 right parenthesis end style to the power of size 14px 2 begin mathsize 14px style left parenthesis left parenthesis f open parentheses x close parentheses plus 1 right parenthesis squared right parenthesis end style to the power of size 14px 1 over size 14px 2 end exponent size 14px equals begin mathsize 14px style left parenthesis left parenthesis log open parentheses x close parentheses plus 1 right parenthesis squared right parenthesis end style to the power of size 14px 1 over size 14px 2 end exponent size 14px f begin mathsize 14px style left parenthesis x right parenthesis end style size 14px plus size 14px 1 size 14px equals size 14px log begin mathsize 14px style left parenthesis x right parenthesis end style size 14px plus size 14px 1 size 14px f begin mathsize 14px style left parenthesis x right parenthesis end style size 14px plus size 14px 1 size 14px minus size 14px 1 size 14px equals size 14px log begin mathsize 14px style left parenthesis x right parenthesis end style size 14px plus size 14px 1 size 14px minus size 14px 1 size 14px f begin mathsize 14px style left parenthesis x right parenthesis end style size 14px equals size 14px log begin mathsize 14px style left parenthesis x right parenthesis end style size 14px left parenthesis size 14px f begin mathsize 14px style left parenthesis x right parenthesis end style size 14px plus size 14px 1 size 14px right parenthesis to the power of size 14px 2 size 14px equals begin mathsize 14px style left parenthesis l o g open parentheses x close parentheses plus 1 right parenthesis end style to the power of size 14px 2 begin mathsize 14px style left parenthesis left parenthesis f open parentheses x close parentheses plus 1 right parenthesis squared right parenthesis end style to the power of size 14px 1 over size 14px 2 end exponent size 14px equals begin mathsize 14px style left parenthesis left parenthesis log open parentheses x close parentheses plus 1 right parenthesis squared right parenthesis end style to the power of size 14px 1 over size 14px 2 end exponent size 14px f begin mathsize 14px style left parenthesis x right parenthesis end style size 14px plus size 14px 1 size 14px equals size 14px log begin mathsize 14px style left parenthesis x right parenthesis end style size 14px plus size 14px 1 size 14px f begin mathsize 14px style left parenthesis x right parenthesis end style size 14px plus size 14px 1 size 14px minus size 14px 1 size 14px equals size 14px log begin mathsize 14px style left parenthesis x right parenthesis end style size 14px plus size 14px 1 size 14px minus size 14px 1 size 14px f begin mathsize 14px style left parenthesis x right parenthesis end style size 14px equals size 14px log begin mathsize 14px style left parenthesis x right parenthesis equals to the power of 10 log left parenthesis x right parenthesis end style  

 

begin mathsize 14px style f left parenthesis 0 comma 0001 right parenthesis equals to the power of 10 log space left parenthesis 0 comma 0001 right parenthesis f left parenthesis 0 comma 0001 right parenthesis equals to the power of 10 to the power of 1 end exponent log space 10 to the power of negative 4 end exponent f left parenthesis 0 comma 0001 right parenthesis equals negative 4 end style(Sifat Logaritma begin mathsize 14px style blank to the power of a to the power of n end exponent log space a to the power of m equals m over n end style)

 

Jadi, jawaban yang tepat adalah D.

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