[Rovers]

1. กำหนด f(x) = x+5 , (gof)(x) = x² - 25 จงหา (f+g)(x) , (f-g)(x) , (fทg)(x) , (f/g)(x)

solve

(gof)(x) = g(f(x)) = g(x+5)
g(x+5) = x² - 25 = (x+5)(x-5) = (x+5)(x+5-10)
g(x) = x(x-10) = x² - 10x

1.1 (f+g)(x)
= f(x) + g(x)
= (x+5) + (x²-10x)
= x² - 9x +5
1.2 (f-g)(x)
= f(x) - g(x)
= (x+5) - (x²-10x)
= 11x + 5 - x²
1.3 (fทg)(x)
= f(x)g(x)
= (x+5)(x²-10x)
= x³ - 5x² - 50x
1.4 (f/g)(x)
= f(x)/g(x)
= (x+5) / (x²-10x) , x น 0,10

2. กำหนด f(2x-3) = 3x-2 และ (f+g)(x) = x²+x-3 จงหา (fog)(x) , (gof)(x), (f-g)(x) , (fทg)(x) , (f/g)(x) และ (g/f)(x)

solve

f(2x-3) = 3x-2 = (3(2x-3)+5)/2
f(x) = (3x+5)/2
(f+g)(x) = f(x)+g(x) = x²+x-3
g(x) = x²+x-3 - ((3x+5)/2) = (2x²-x-11)/2