Let #f(x) = 3x - 4# and #g(x) = x^2 - 2#, what is the value of #f(g(2))# and #f(g(x))#?

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Answer 1 · 2016-03-04T22:46:19

#color(blue)(f(g(2))=2)#
#color(white)(.)#
#color(blue)(g(f(x))= -15x+14)#

Assuming you mean:
#f(x)=3x-4#
#g(x)=x^2-2#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("To determine "f(g(2)))#

#g(2)=2^2-2" " =" "4-2" "=" "2 #

#f(g(2))=3(2)-4" " =" "6-4" "=" "2#

#color(blue)(f(g(2))=2)#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("To determine "g(f(x)))#

Given that #f(x)=3x-4# then

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

#g(f(x))= (9x-24x+16)-2#

#color(blue)(g(f(x))= -15x+14)#