Question #55f42

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Answer 1 · 2017-04-09T10:59:13

#f@g(x)=3x^2+4#
#g@f(x)=9x^2-12x+6#

Given:

#g(x)=x^2+2#
#f(x)=3x-2#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#f@g(x)#

Where ever there is an #x# in #f(x)# write #x^2+2#

#f(color(red)(x))=3color(red)(x)-2" "->" "3(color(red)(x^2+2))-2#

#" "->" "3x^2+4#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#g@f(x)#

Where ever there is an #x# in #g(x)# write #3x-2#

#g(color(red)(x))=color(red)(x)^2+2" "->" "(color(red)(3x-2))^2+2#

#" "->" "9x^2-12x+4+2#

#" "->" "9x^2-12x+6#

Answer 2 · 2017-04-09T11:08:28

#f (g(x)) = 3x^2 +4# ,
#g (f(x)) = 9x^2-12x+6#

#f(x) = 3x-2 ; g(x) =x^2+2#
#f (g(x)) = f (x^2+2) =3 (x^2+2) -2= 3x^2 +4#

#g (f(x)) = g(3x-2) = (3x-2)^2 +2 = 9x^2 -12 x +4 +2 = 9x^2-12x+6# [Ans]