What is equal to #(f-g)(-5)? color(white)("d") # #color(white)("d")# #f(x)=2+x", "color(white)("d")g(x)=x^2+5#

1 Answer
Jan 9, 2018

#-33#

Explanation:

#color(blue)("Preamble")#

Note that #f and g# are just names. The question poser has assigned those names to the equation structures given.

So within the context OF THIS QUESTION whenever you see the name #g# you know they are talking about #x^2+5#
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#color(blue)("Answering the question")#

Set #y_1=f( color(red)(x))=2+color(red)(x) #

So by substituting (-5) for #x# we have:

#y_1=f( color(red)(-5))=2+(color(red)(-5)) =-3 #
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Set #y_2=g(color(red)(x))=color(red)(x)^2+5#

So by substituting (-5) for #x# we have:

Set #y_2=g(color(red)(-5))=(color(red)(-5))^2+5 = +30#

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#(f-g)(-5)color(white)("d")=color(white)("d")y_1-y_2color(white)("ddd")=color(white)("ddd")-3-30color(white)("d")=color(white)("d")-33#