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

Answer 1

To find ( f(g(x)) ), substitute the function ( g(x) ) into ( f(x) ). So, ( f(g(x)) = f(3x + 1) ). Then, wherever there is an ( x ) in ( f(x) ), replace it with ( 3x + 1 ). Thus, ( f(g(x)) = (3x + 1)^2 - (3x + 1) ). This simplifies to ( f(g(x)) = 9x^2 + 6x + 1 - 3x - 1 ), which further simplifies to ( f(g(x)) = 9x^2 + 3x ).

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Answer 2

Hazel Anglin

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

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#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.