Question

Let `u(x)=e^(9x)` and `v(x)=5x+9`, how do you find `(v(u(x)))^2`?

Answer 1

Be `y = u(x) = e^(9x)`

`rarr v(u(x)) = v(y) = 5y+9 = 5e^(9x)+9`

`rarr (v(u(x)))^2 = (v(y))^2 = (5y+9)^2`

`= (5y+9)(5y+9) = (5*5*y*y)+(5*y*9)+(9*5*y)+(9*9)`

`= 25y^2+90y+81`

`= 25(e^(9x))^2+90e^(9x)+81`

`= 25e^(2*9x)+90e^(9x)+81`

`= 25e^(18x)+90e^(9x)+81`