Fungsi invers 1. Di ketahui (g°f)(x)= 4x2+4x dan g(x)= x2-1 tantukan nilai f(x-2) 2. f(x) = √x2+1 d.... Question from @destra

Takamori37 1.
$(gof)(x)=4x^2+4x,g(x)=x^2-1 \\ g(f(x))=4x^2+4x \\ (f(x))^2-1=4x^2+4x \\ (f(x))^2=4x^2+4x+1 \\ f(x)= \sqrt{(2x+1)^2}=2x+1 \\ f(x-2)=2(x-2)+1=2x-4+1=2x-3$
2.
$(fog)(x)=\displaystyle\frac{1}{x-2} \sqrt{x^2-4x+5} \\ y=\displaystyle\frac{\sqrt{x^2-4x+5}}{x-2}=\sqrt{\displaystyle\frac{{x^2-4x+5}}{(x-2)^2}}=\sqrt{\displaystyle\frac{{x^2-4x+5}}{x^2-4x+4}} \\ y^2=\displaystyle\frac{{x^2-4x+5}}{x^2-4x+4} \\ . \\ x^2y^2-4xy^2+4y^2=x^2-4x+5 \\ x^2y^2-x^2-4xy^2+4x+4y^2-5=0 \\ x^2(y^2-1)-4x(y^2-1)+4(y^2-1)-1=0 \\ x^2(y^2-1)-4x(y^2-1)+4(y^2-1)=1 \\ (y^2-1)(x^2-4x+4)=1 \\ x^2-4x+4=\displaystyle\frac{1}{y^2-1} \\ (x-2)^2=\displaystyle\frac{1}{y^2-1}$
$(x-2)^2=\displaystyle\frac{1}{y^2-1} \\ x-2=\pm \displaystyle\frac{1}{\sqrt{y^2-1}} \\ x=2\pm\frac{1}{\sqrt{y^2-1}} \\ (fog)^{-1}(x)=2\pm\frac{1}{\sqrt{x^2-1}}$

3 votes Thanks 1

destra makasihh :D :D

destra nmr 2 di foto bsa gakk hehehehe ...

Takamori37 Serius itu soalnya dicari (fog)-1(x) ?

destra iiya (fog)invers (x) , emm maksudnya -1 itu pngkat -1

Takamori37 Iya

Takamori37 Bener gak ?

destra makasihh yaaaa .... , makasihh bangettttttt ... :D :D :D

Takamori37 Sip deh

RichadAgustinusKD A4x-1/2
b. itu kurungnya bagaimana semua atau X nya doang

0 votes Thanks 0

destra kurung yang mananya ??

RichadAgustinusKD fog

destra iiya x nya doang

RichadAgustinusKD yang itu X pangkat 2 ya (FOG)

RichadAgustinusKD a ) 2X-3

destra iyya ...

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