Find (fog) if f(x)=x^3+1 and g(x)=x+1?

### 1 Answer | Add Yours

To determine the result of compositions of the given function, all we need to do is to plug in the second function listed g(x) into the first function f(x).

Conclusion: We'll replace x by g(x) in the expression of f(x).

(fog)(x) = [f(g(x))] = [g(x)]^3 + 1

(fog)(x) = (x+1)^3 + 1

This sum of cubes returns the product:

a^3 + b^3 = (a+b)(a^2 - ab + b^2)

(x+1)^3 + 1 = (x + 1 + 1)[(x+1)^2 - x - 1 + 1]

(x+1)^3 + 1 = (x+2)(x^2 + 2x + 1 - x - 1 + 1)

We'll eliminate like terms within the second pair of brackets:

(x+1)^3 + 1 = (x+2)(x^2 + x + 1)

(x+1)^3 + 1 = x^3 + x^2 + x + 2x^2 + 2x + 2

(x+1)^3 + 1 = x^3 + 3x^2 + 3x + 2

**The result of combining the given functions f and g is: (fog)(x) = x^3 + 3x^2 + 3x + 2.**

### Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes