Pertanyaan

.Diketahui f ( x ) = 2 − x dan ( g ∘ f ) ( x ) = 2 x − 3 x . Tentukan g ( x ) .

.Diketahui $f (x) = 2 - x$ dan $(g \circ f) (x) = \frac{x}{2 x - 3}$ . Tentukan $g (x)$ .

F. Ayudhita

Master Teacher

Jawaban terverifikasi

Jawaban

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell bold italic g bold left parenthesis bold x bold right parenthesis end cell bold equals cell fraction numerator bold italic x to the power of bold 2 bold minus bold 4 bold italic x bold plus bold 4 over denominator bold 2 bold italic x to the power of bold 2 bold minus bold 8 bold italic x bold plus bold 5 end fraction end cell end table end style$

Pembahasan

Ingat! artinya dimasukkan ke Berdasarkan konsep tersebut maka Misalkan sehingga maka Jadi,

Ingat!

artinya dimasukkan ke

Berdasarkan konsep tersebut maka

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses g ring operator f close parentheses open parentheses x close parentheses end cell equals cell g open parentheses f open parentheses x close parentheses close parentheses end cell row cell fraction numerator x over denominator 2 x minus 3 end fraction end cell equals cell g open parentheses 2 minus square root of x close parentheses end cell end table end style$

Misalkan sehingga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 minus square root of x end cell equals p row cell negative square root of x end cell equals cell p minus 2 end cell row x equals cell open parentheses p minus 2 close parentheses squared end cell end table end style

maka

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell g open parentheses 2 minus square root of x close parentheses end cell equals cell fraction numerator x over denominator 2 x minus 3 end fraction end cell row cell g open parentheses p close parentheses end cell equals cell fraction numerator open parentheses p minus 2 close parentheses squared over denominator 2 open parentheses p minus 2 close parentheses squared minus 3 end fraction end cell row blank equals cell fraction numerator p squared minus 4 p plus 4 over denominator 2 open parentheses p squared minus 4 p plus 4 close parentheses minus 3 end fraction end cell row blank equals cell fraction numerator p squared minus 4 p plus 4 over denominator 2 p squared minus 8 p plus 8 minus 3 end fraction end cell row blank equals cell fraction numerator p squared minus 4 p plus 4 over denominator 2 p squared minus 8 p plus 5 end fraction end cell end table end style$

Jadi, $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell bold italic g bold left parenthesis bold x bold right parenthesis end cell bold equals cell fraction numerator bold italic x to the power of bold 2 bold minus bold 4 bold italic x bold plus bold 4 over denominator bold 2 bold italic x to the power of bold 2 bold minus bold 8 bold italic x bold plus bold 5 end fraction end cell end table end style$