Question

The functions u and w are defined as follows.Find the value of u(w(3)) .w(x) = - x ^ 2 - 1u(x) = x + 2

Answer 1

Given:

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

Aim:

`We\text{ need to find u\lparen w\lparen3\rparen\rparen.}`

Step-by-step explanation:

`w(x)=-x^2-1`

Substitute x =3 in the equation w(x).

`w(3)=-(3)^2-1`

`w(3)=-9-1`

`w(3)=-10`

Substitute w(3)=-10 in the expression u(w(3)).

`u(w(3))=u(-10).`

Substitute x =-10 in the eqaution u(x).

`u(-10)=-10+2`

`u(-10)=-8`

`Use\text{ }u(-10)=-8\text{ in the equation u\lparen w\lparen3\rparen\rparen=u\lparen-10\rparen.}`

`u(w(3))=u(-10)=-8`

`u(w(3))=-8`

Final answer:

`u(w(3))=-8`