Question

Let f(x) = 4x2 + x + 1 and g(x) = x2 – 2

Answer 1

To find  g (f(x))  you  should  substitute  "4x^2+x+1"   to  "x"  of  g(x)  function. You'll havew:

$g(f(x))= (4x^2+x+1)^2-2=\\ \\ =(4x^2+x)^2 +2 \cdot (4x^2+x) \cdot 1 +1^2-2= \\ \\ = 16x^4+8x^3+x^2+8x^2+2x+1-2= \\ \\ = 16x^4+8x^3+9x^2+2x-1$

To count (4x^2+x+1)^2  Just  assume  ( [4x^2+x] + 1)^2   and  use the (a+b)^2=a^2+2ab+b^2  formula, where a=4x^2+x  and  b=1