Diketahui - Universityku

f(x) = x²-25
g(x) = x²-2 – 2x – 15
h (x)=3x²-x+12
Tentukan
a. f + g
b. h – g
c. f.h
d. g/h

Diketahui

$f(x) = {x}^{2} - 25$

$g(x) = {x}^{2} - 2x - 15$

$h(x) = 3 {x}^{2} - x + 12$

SOAL A.

$(f + g)(x) = f(x) + g(x)$

$(f + g)(x) = ( {x}^{2} - 25) + ( {x}^{2} - 2x - 15)$

$(f + g)(x) = {x}^{2} - 25 + {x}^{2} - 2x - 15$

$(f + g)(x) = {x}^{2} + {x}^{2} - 2x - 25 - 15$

$(f + g)(x) = 2 {x}^{2} - 2x - 40$

SOAL B.

$(h - g)(x) = h(x) - g(x)$

$(h - g)(x) = (3 {x}^{2} - x + 12) - ( {x}^{2} - 2x - 15)$

$(h - g)(x) = 3 {x}^{2} - x + 12 - {x}^{2} + 2x + 15$

$(h - g)(x) = 3 {x}^{2} - {x}^{2} - x + 2x + 12 + 15$

$(h - g)(x) = 2 {x}^{2} + x + 27$

SOAL C.

$(f times h)(x) = f(x) times h(x)$

$(f times h)(x) = ( {x}^{2} - 25)(3 {x}^{2} - x + 12)$

$(f times h)(x) = 3 {x}^{4} - {x}^{3} + 12 {x}^{2} - 75 {x}^{2} + 25x - 300$

$(f times h)(x) = 3 {x}^{4} - {x}^{3} - 63 {x}^{2} + 25x - 300$

SOAL D.

$( frac{g}{h} )(x) = frac{g(x)}{h(x)}$

$( frac{g}{h} )(x) = frac{( {x}^{2} - 2x - 15) }{(3 {x}^{2} - x + 12)}$