[Rovers]

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)

solve

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)

solve

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