Question

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

u(x)=x^2 + 6
w(x)= square root of x+1

Find the following...

(u•w)(3)
(w•u)(3)

Answer 1

(u•w)(3) = 10

(w•u)(3) = 4

Explanation:

u(x) = x² + 6

w(x) = √(x + 1)

(u•w)(x) = u(w(x))

(u•w)(x) = (w(x))² + 6

(u•w)(x) = (√(x + 1))² + 6

(u•w)(x) = x + 1 + 6

(u•w)(x) = x + 7

(u•w)(3) = 3 + 7

(u•w)(3) = 10

(w•u)(x) = w(u(x))

(w•u)(x) = √(u(x) + 1)

(w•u)(x) = √(x² + 6 + 1)

(w•u)(x) = √(x² + 7)

(w•u)(3) = √(3² + 7)

(w•u)(3) = 4