F(x) = x^2. What is g(x)?

This becomes way easier if you have the knowledge of inverse functions.

Let me make this clear. You have f(x)=x2+1 f(x)=x2+1 and g(f(x))=1/(x2+4)g(f(x))=1/(x2+4). Now pause and think about the second function. The function is defined as g(f(x))g(f(x)), right. now what if there is some way that you could manipulate this function and some how change it to g(x)g(x). Or think about with what other function should you multiply f(x)f(x) [the function in g(f(x))g(f(x)) ] to get xx [so that the function would be g(x)g(x)]. It is f(x)−1f(x)−1 right.

So let us find f(x)f(x) inverse. f(x)=x2+1f(x)=x2+1 then f(x)−1=x−1−−−−−√f(x)−1=x−1 right [ just swipe the xx with f(x)

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0