If #f(x)=3x# and #g(x)=4x-3#, how do you find f[g(5)] and g[f(5)]?

1 Answer
Alan P.
Jul 23, 2015

Evaluate #a = g(5)# then substitute the value of #a# for the argument #g(5)# in #f(g(5))# and evaluate #f(a)# for this argument.
(Similarly for #g(f(5))#)

Explanation:

#f(x)=3x##color(white)("XXXXXX")##rarr##color(white)("XXXX")##f(5) = 15#

#g(x) = 4x-3##color(white)("XXXX")##rarr##color(white)("XXXX")##g(5) = 17#

#f(g(5)) = f(17)#
#color(white)("XXXX")##= 3(17) = 51#

#g(f(5) = g(15)#
#color(white)("XXXX")##= 4(15) -3 = 57#

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