Questions: Knowledge Check Question 11 The functions (u) and (w) are defined as follows. (u(x)=-x+1) (w(x)=x^2-2) Find the value of (w(u(4))). (w(u(4))=) (square) (sqrtsquare) (square) (square) 5 I Don't Know Submit

Knowledge Check Question 11 The functions (u) and (w) are defined as follows. (u(x)=-x+1) (w(x)=x^2-2) Find the value of (w(u(4))). (w(u(4))=) (square) (sqrtsquare) (square) (square) 5 I Don't Know Submit
Transcript text: Knowledge Check Question 11 The functions $u$ and $w$ are defined as follows. \[ \begin{array}{l} u(x)=-x+1 \\ w(x)=x^{2}-2 \end{array} \] Find the value of $w(u(4))$. \[ w(u(4))= \] $\square$ \[ \sqrt{\square} \] $\square$ $\qquad$ $\square$ 5 I Don't Know Submit
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Solution

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Solution Steps

Step 1: Evaluate u(4) u(4)

The function u(x) u(x) is defined as u(x)=−x+1 u(x) = -x + 1 . We need to find u(4) u(4) .

u(4)=−(4)+1=−4+1=−3 u(4) = -(4) + 1 = -4 + 1 = -3

Step 2: Evaluate w(u(4)) w(u(4))

Now that we have u(4)=−3 u(4) = -3 , we need to find w(−3) w(-3) using the function w(x)=x2−2 w(x) = x^2 - 2 .

w(−3)=(−3)2−2=9−2=7 w(-3) = (-3)^2 - 2 = 9 - 2 = 7

Final Answer

The value of w(u(4)) w(u(4)) is 7\boxed{7}.

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