To evaluate the composite function u(w(2)): 1) The inner function w(x) = 1/(x-1) is evaluated at x = 2, giving w(2) = 1. 2) This value of 1 is substituted into the outer function u(x) = x^2 + 3x + 2, giving u(1) = 6. 3) Therefore, the value of the composite function u(w(2)) is 6.

1. Example TwoEvaluate a Composite Function

2. 𝑢𝑥=𝑥2+3x + 2 w(x) = 1𝑥−1 Evaluate u(w(2)) Start with u(x)=𝑥2+3x + 2 2. LS Replace x with w(x). This is simple substitution. You’ll get u(w(x)). Do the same on RS to get: 𝑢𝑤𝑥=1𝑥−12+31𝑥−1+2 3. Q-What do you do to go from u(w(x)) to u(w(2))? A-Replace the x with 2: 𝑢𝑤2=12−12+312−1+2 4. Solve. 12+31+2=6

3. The same can be done in reverse: Reverse: 1) Determine w(2) 𝑤2=12−1 =1 2) Substitute into u(x) 𝑢𝑤2=12+31+2 =6 Previous Way: LS = u(x) = u(w(x)) = u(w(2)) 𝑢𝑥=𝑥2+3x + 2 w(x) = 1𝑥−1