Soal matematika sma

Soal matematika sma

$f(x)=x^2+4x\ g(x)=x-1$

$(f,o,g)(x)=f(g(x))\\ (f,o,g)(x)={(g(x))}^2+4g(x)\\ (f,o,g)(x)={(x-1)}^2+4(x-1)\\ (f,o,g)(x)=(x^2-2x+1)+4x-4\\ (f,o,g)(x)=x^2+3x-3$

$(f,o,g)(x)=4x-1\ g(x)=x^2+4x-2\ f(x)=?$

$(f,o,g)(x)=f(g(x))\\ 4x-1=f(x^2+4x-2)\\ f(x^2+4x-2)=4x-1$

misal,

$y=x^2+4x-2$

maka,

$x=-2+sqrt{y+6}$

Sehingga,

$f(x^2+4x-2)=4x-1\\ f(y)=4(-2+sqrt{y+6})-1\\ f(y)=-8+4sqrt{y+6}-1\\ f(y)=4sqrt{y+6}-9\\ f(x)=4sqrt{x+6}-9$

$f(x)=7x+8\ f^{-1}(x)=,?$

Rumus :

$f(x)=ax+b\\ f^{-1}(x)=frac{x-b}{a}$

Maka,

$f(x)=7x+8\\ f^{-1}(x)=frac{x-8}{7}$

$f(x)=frac{3x-1}{2-x}\ f^{-1}(x)=,?$

Rumus :

$f(x)=frac{ax+b}{cx+d}\\ f^{-1}(x)=frac{-dx+b}{cx-a}$

Maka,

$f(x)=frac{3x-1}{2-x}=frac{3x-1}{-x+2}\\ f^{-1}(x)=frac{-2x-1}{-x-3}=frac{2x+1}{x+3}$