Composition of two functions

Question

Suppose that the functions u and w are defined as follows

u(x)=--x+2

w(x)=x^2+1

Find the following

(w o u) (5) =

(u o w) (5) =

Answer 1

u(x) = 2-x and w(x) = x^2+1

Then

T(x) = w comp u = (2-x)^2 + 1

M(x) = u comp w = 2-(x^2+1)

= 2 - x^2 - 1

= 1 - x^2

T(5) = 10; note that u(5) = -3 and w(-3) = 10

which agrees

M(5) = -24; note that w(5) = 26 and u(26) = 2-26 = -24

which agrees