Question

suppose the functions u and w are defined as follows u(x)=x+9 w(x)=the square root of x+8 find the following (wou)(8)= (uow)(8)=

Answer 1

Explanation:

`u(x)=x+9\\\\w(x)=√(x+8) \\\\(wou)(x)=u(w(x))=u(√(x+8) )=√(x+8)+9\\(wou)(8)= √(8+8)+9=4+9=13\\\\\\(uow)(x)=w(u(x))=w(x+9)=√(x+9+8)=√(x+17)\\(wou)(8)= √(8+17)=√(25)=5\\\\`

Answer 2

5 and 13

Explanation:

To evaluate (w ￮ u)(8) , evaluate u(8) then substitute the value obtained into w(x) , that is

u(8) = = 8 + 9 = 17 , then

w(17) =
`√(17+8)` =
`√(25)` = 5

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To evaluate (u ￮ w )(8) , evaluate w(8) then substitute the value obtained into u(x) , that is

w(8) =
`√(8+8)` =
`√(16)` = 4 , then

u(4) = 4 + 9 = 13