Question

PLS SOLVE ASAP. I will mark brainlest.

Answer 1

Answer:

• $(w \cdot u) (7)$ =  $\bf 8$

• $(u \cdot w) (7)$  =  $\bf 22$

Step-by-step explanation:

We are given:

$u(x) = x^2 + 6$

$w(x) = \sqrt{x + 9}$.

• $(w \cdot u) (7)$. read as "w of u of 7", means we have to input 7 into the function $u(x)$, and use the output we get as input for the function $w(x)$ :

$(w \cdot u) (7)$

⇒ $w(u(7))$

⇒ $w(7^2 + 6)$

⇒ $w(55)$

⇒ $\sqrt{55 + 9}$

⇒ $\sqrt{64}$

⇒ $\bf 8$

• Similarly, we can evaluate $(u \cdot w) (7)$ :

$(u \cdot w) (7)$

⇒ $u(w(7))$

⇒ $u(\sqrt{7 + 9})$

⇒ $u(\sqrt{16})$

⇒ $u(4)$

⇒ $4^2 + 6$

⇒ $\bf 22$

Answer 2

The answers are :

(w o u)(7) = 8

(u o w)(7) = 22

To find the first answer, substitute u(x) in w(x), and set x = 7.

• u(7) = 7² + 6
• u(7) = 49 + 6
• u(7) = 55

• w(u(7)) = √(55 + 9)
• w(u(7)) = √64
• w(u(7)) = 8
• (w o u)(7) = 8

To find the second answer, substitute w(x) in u(x), and set x = 7.

• w(7) = √(7 + 9)
• w(7) = √16
• w(7) = 4

• u(w(7)) = 4² + 6
• u(w(7)) = 16 + 6
• u(w(7)) = 22
• (u o w)(7) = 22