If #f(x) = x^2 - x# and #g(x) = 3x + 1# how do you find f(g(x))?

1 Answer
May 12, 2016

#f(g(x))=color(green)(3x^2+3x#

Explanation:

The problem with this type of question is often the confusion that results from two different uses of #x#

If instead we write
#color(white)("XXX")f(color(blue)(w))=color(blue)(w)^2-color(blue)(w)#
then there is less difficulty in replacing #color(blue)(w)# with #color(red)(g(x))#
#color(white)("XXX")f(color(red)(g(x)))=color(red)(g(x))^2-color(red)(g(x))#
and then replacing #color(red)(g(x))# with #color(brown)(3x+1)#
#color(white)("XXX")f(g(x)) = (color(brown)(3x+1))^2-(color(brown)(3x+1))#

#color(white)("XXXXXXX")=3x^2+6x+1-3x-1#

#color(white)("XXXXXXX")=3x^2+3x#