(u∘w)(4)=−34
(w∘u)(4)=72
Given the functions u(x)=−x−2 and w(x)=2x^2 , you're asked to find the compositions
(u∘w)(4) and (w∘u)(4).
Find (u∘w)(4):
(u∘w)(4)=u(w(4))
First, find w(4):
w(4)=2×(4)^2 =2×16=32
Now, substitute this result into u(x):
(u∘w)(4)=u(32)=−32−2=−34
Therefore, (u∘w)(4)=−34.
Find (w∘u)(4):
(w∘u)(4)=w(u(4))
First, find u(4):
u(4)=−4−2=−6
Now, substitute this result into w(x):
(w∘u)(4)=w(−6)=2×(−6)^2 =2×36=72
Therefore, (w∘u)(4)=72.
In summary:
(u∘w)(4)=−34
(w∘u)(4)=72
These compositions involve applying one function to the result of another function at the specified value.
Question
Suppose that the function u and w are defined as follows.
u(x)= - x - 2
w(x)= 2 x^2
Find the following.
(u o w) (4)=__
(w o u) (4)=__