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Can someone help me answer the second one

Can someone help me answer the second one-example-1
User Synepis
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1 Answer

5 votes

Answer:


(u \circ \; w)(2) = \boxed{7}


(w \circ \;u)(2) = \boxed{3}

Explanation:

We have the two functions as


u(x) = x^2 + 3\\\\w(x) = √(x + 2)


(u \circ w)(x) also written as
u(w(x)) is the composite function; it means that

x = w(x) should be substituted in
u(x)

To determine
(u \circ w)(x), simply substitute the expression for
w(x) wherever there is an x in
u(x)

For a specific value of x, in this case x = 2,

  • first find w(x2)
  • substitute this value for x in u(x)


Part 1

(u \circ w)(2):\\\\w(2) = √(2 + 2) = 4(u \circ w)(2) = 2^2 + 3 = 4 + 3 = 7

For
(w \circ u)(x), we substitute the expression for
u(x) into
w(x) wherever an
x appears in
w(x)

For a specific value of x, say 2, find the value of u(2) and substitute it into
w(x)


u(2) = 2^2 + 3 = 7


(w \circ u)(2), = √(7 + 2) = √(9) = 3\\



User Padibro
by
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