Question

u(x) = 4x - 2 w(x) = - 5x + 3The functions u and w are defined as follows.Find the value of u(w(- 3)) .

Answer 1

- We are given the two functions below:

`\begin{gathered} u(x)=4x-2 \\ \\ w(x)=-5x+3 \end{gathered}`

- We are asked to find u(w(-3)).

- In order to find u(w(-3)), we need to first find u(w(x)) and then we can substitute x = -3.

- Since we have been given u(x), then, it means that we can find u(w) as follows:

`\begin{gathered} u(x)=4x-2 \\ u(w),\text{ can be gotten by substituting w for x} \\ \\ u(w)=4w-2 \end{gathered}`

- But we have an expression for w in terms of x. This means that we can say:

`\begin{gathered} u(w)=4w-2 \\ \\ w(x)=-5x+3 \\ \\ \therefore u(w(x))=4(-5x+3)-2 \\ \\ u(w(x))=-20x+12-2 \\ \\ \therefore u(w(x))=-20x+10 \end{gathered}`

- Now that we have an expression for u(w(x)), we can proceed to find u(w(-3)) as follows:

`\begin{gathered} u(w(x))=-20x+10 \\ put\text{ }x=-3 \\ \\ u(w(-3))=-20(-3)+10 \\ \\ u(w(-3))=60+10=70 \end{gathered}`

Final Answer

The answer is

`u(w(-3))=70`