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พีชคณิตของฟังก์ชัน
1. กำหนด f(x) = x+5 , (gof)(x) = x2 - 25 จงหา (f+g)(x) , (f-g)(x) , (fทg)(x) , (f/g)(x)
(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) 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 |
3. กำหนด f-1(x+1) = 2x+3 และ (fog)(x-1) = 5x+1
จงหา (f+g)(1) , (f+g)-1(1) , ((fทg)of-1)(1) , (f/g + f-1)(3) f-1(x+1) = 2x+3 = 2(x+1)+1 f-1(x) = 2x+1 f(x) = (x-1)/2 (fog)(x-1) = f(g(x-1)) = (g(x-1)-1)/2 = 5x+1 g(x-1) = 10x+3 = 10(x-1) +13 g(x) = 10x+13 (f+g)(x) = f(x)+g(x) = (21x+25)/2 \ (f+g)-1(x) = (2x-25)/21 4. กำหนด f(x) = 3x+5 , g(x) = 2x+1 จงหา 4.1 (f-1+g-1)(5) 4.2 (f-1-g-1)(10) 4.3 (f-1ทg-1)(-5) 4.4 (f-1/g-1)(-10) f(x) = 3x+5 f-1(x) = (x-5)/3 g(x-1) = 2x+1 = 2(x-1)+3 g(x) = 2x+3 g-1(x) = (x-3)/2 |
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