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)?

Question

2008 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-24T01:32:22

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#