Question

Let f(x) = 4x2 + x + 1 and g(x) = x2 – 2. Find g(f(x)). Show each step of your work. Help please

Answer 1

Answer: The answer is $16x^4+8x^3+9x^2+2x-1.$

Step-by-step explanation: The given functions f(x) and g(x) are defined as follows:

$f(x)=4x^2+x+1,\\\\g(x)=x^2-2.$

We are given to evaluate g(f(x)).

The steps are as follws:

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

Thus, the answer is $16x^4+8x^3+9x^2+2x-1.$

Answer 2

For the answer to the question above, 
g(f(x)) = (4x^2 + x + 1)^2 - 2 

g(f(x)) = (16x^4 + 4x^3 + 4x^2 + 4x^3 + x^2 + x + 4x^2 + x + 1) - 2 

g(f(x)) = 16x^2 + 8x^3 + 9x^2 + 2x + 1 - 2 

g(f(x)) = 16x^2 + 8x^3 + 9x^2 + 2x - 1
I hope my answer helped you. Feel free to ask more questions. Have a nice day!