how do I solve this

Question

Suppose that the functions u and w are defined as follows.

u(x)= x²+6

w(x)= √x+1

find the following

(w · u)(3)

(u · w)(3)

Answer 1

u = x^2 +6

u(3) = 9+6 = 15

w = sqrx +1

w(3) = sqr3 + 1

w*u(3) = w(3)*u(3) = (sqr3+1)(15) = 15sqr3 + 15

or

w*u (x^2 +6)(sqr(x) +1)

= x^(2.5) + x^2 + 6x^(1/2) + 6

w*u(3) = 3^(2.5) + 3^2 + 6(3)^(1/2) + 6

= 3^(2.5) + 9 + 6sqr3 +6

= 9sqr3 +6sqr3 +9+6

= 15sqr3 + 15

u*w(3) = the same as w*u(3)

UNLESS you meant a composite function by the dot and not multiplication

then there's a difference:

u(w(3)) = (sqr3+1)^2 + 6 = 3 +2sqr3 +1 +6 = 10+2sqr3

= about 10+2(1.732) = 13.464

w(u(3)) = sqr(15) +1

= about 18.873

that the problem suggests there's a possible difference, suggests it wanted composite functions for the dot

composite functions will be the same = x each, if they are inverse functions: f(f^-1)(x)) = x