1 Answer

Padibro · Answer 1 · 2024-12-22T10:24:53+0000

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,

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
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

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

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