Jika (f 0 g) (x)=x²+3x+4 dan g(x)=4x-5 tentukan rumus f(x)?​

By Posted on

Jika (f 0 g) (x)=x²+3x+4 dan g(x)=4x-5 tentukan rumus f(x)?​

(fog)(x) = (x² + 3x + 4)

f(g(x)) = (x² + 3x + 4)

f(4x – 5) = (x² + 3x + 4)

Misalkan, y = (4x – 5). Maka x = frac{(y + 5)}{4}

f(y) = ( { frac{(y + 5)}{4}) }^{2} + 3( frac{(y + 5)}{4} ) + 4

f(y) = ( frac{ {y}^{2} + 10y + 25}{16} ) + ( frac{3y + 15}{4} ) + 4

f(y) = frac{( {y}^{2} + 10 y + 25) + (12y + 60) + 64}{16}

f(y) = frac{ {y}^{2} + 10y + 12y + 25 + 60 + 64}{16}

f(y) = frac{ {y}^{2} + 22y +149 }{16}

Ubahlah variabel y menjadi variabel x. Maka

f(x) = frac{ {x}^{2} + 22x + 149 }{16}