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Given the following functions; u(x) = x^2+9 w(x) = #sqrt(x+8)# How does one determine (w#@#u)(8) and (u#@w#)(8)?

Answer 1

Elias Ackerman

To find #(w@u)(8)#,

evaluate #u(x)# when #x = 8#:

#u(x) = x^2+8#

#u(8) = 8^2+8#

#u(8) = 72#

then evaluate #w(x)# when #x = 72#:

#w(x) = sqrt(x+8)#

#w(72) = sqrt(72+8)#

#w(72) = sqrt(80)#

#w(72) = 4sqrt5#

#(w@u)(8)= 4sqrt5#

To find #(u@w)(8)#,

evaluate #w(x)# when #x = 8#:

#w(x) = sqrt(x+8)#

#w(8) = sqrt(8+8)#

#w(8) = sqrt16#

#w(8) = 4#

then evaluate #u(x)# when #x = 4#:

#u(x) = x^2+8#

#u(4) = 4^2+8#

#u(4) = 16+8#

#u(4) = 24#

#(u@w)(8) = 24#

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Answer 2

Theodore Amidon

To determine (w@u)(8) and (u@w)(8), you need to perform function composition. This involves substituting the function w into u and vice versa, then evaluating the resulting composite functions at the given value of x, which is 8 in this case.

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Answer from HIX Tutor

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