Question

•f(x-5)=2x-5
•g(x)=2x-1/3x+2
(f°g)=. . . ?
(g°f)=. . . ?

Answer 1

F(x-5)= 2x - 5
f(x) = 2(x+5) - 5
f(x) = 2x + 10 - 5
f(x) = 2x + 5

g(x)= (2x -1)/(3x+2)

fog(x) = f{ g(x) } = f{ (2x -1)/(3x+2)}
fog(x)= 2 {(2x-1) /(3x + 2)} + 5
fog(x)= (4x-2)/(3x+2)  + 5
fog(x)= {(4x-2)+5(3x+2)}/(3x+2)
fog(x)= (4x-2+15x+10)/(3x+2)
fog(x)= (19x + 8)/(3x+2)

gof(x)= g{f(x)} = g(2x+5)
gof(x)= {2(2x+5) - 1}/{3(2x+5) + 2}
gof(x)= (4x+10-1)/(6x+15+2)
gof(x)= (4x+9)/(6x+17)