If #f(x)=x^2+4x# and #g(x)=3x-5#, how do you find #(f(g(x))# and #g(f(x))#?

1 Answer
Alan P.
Feb 19, 2015

It might be better if we think of the functions as having different parameters, so

If #f(a)=a^2+4a#
and #g(b)=3b−5#,

then
#f(g(x))# simply means re-writing the #f(a)# equation with #a# replaced by #g(x)#:
#f(g(x))#
# = (g(x)^2 + 4(g(x))#
# = (3x - 5)^2 + 4(3x -5)#
# = 9x^2 -18x +5#

Similarly
#g(fx))#
# = 3(x^2 + 4x) - 5# (by replacing #b# with #f(x)#)
# = 3x^2 + 12x#

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