If #f(x) = x^2 + 3x# and #g(x) = 4x - 1#, what is #(g@f)(x)#?

1 Answer
Alan P.
May 28, 2015

#(g@f)(x)# (sometimes written #g(f(x))#)

can be expressed by
writing the equation for #g(x)#
then replacing each occurrence of #x# in this equation with the expression for #f(x)#

#g(color(red)(x)) = 4color(red)(x)-1#

replacing each #color(red)(x)# with the expression for #f(x)#, namely #color(blue)(x^2+3x)#

#g(f(x)) = 4(color(blue)(x^2+3x))-1 #

#= 4x^2+12x - 1#

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