Question

Question?
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Answer 1

f(x) = 4x+1
g(x)= x^2 - 2

f( g(x) ) is short for "replace "x" with g(x)
you start with
f(x) = 4x+1

replace x with g(x)
f( g(x) ) = 4 g(x) +1

now replace g(x) with its "expanded form" (x^2-2)
be sure to keep the parens.
what do you get ?

Answer 2

4(x^2-2)+1 (x^2-2)

Answer 3

you only have one g(x) in 4 g(x) + 1

f( g(x) ) = 4 g(x) +1
^
|
this is replaced with (x^2-2)
the +1 stays as is

Answer 4

g(x) is short-hand for (x^2-2), and we are expanding the g(x) into its "full name"

Answer 5

=4x^2 -8+1

Answer 6

yes, and notice you can simplify -8+1 to -7