Question

If f(x)=x⁴-x³+x² and g(f)=-x², where x can not equal 0, what is (f/g)(x)?

Answer 1

`\displaystyle ((f)/(g))(x) = -(x^2 - x + 1)`

General Formulas and Concepts:

Algebra I

• Terms/Coefficients
• Factoring
• Functions
• Function Notation

Explanation:

Step 1: Define

Identify

`\displaystyle f(x) = x^4 - x^3 + x^2`

`\displaystyle g(x) = -x^2`

Step 2: Find

1. Substitute in function values:
   `\displaystyle ((f)/(g))(x) = (x^4 - x^3 + x^2)/(-x^2)`
2. Factor:
   `\displaystyle ((f)/(g))(x) = (x^2(x^2 - x + 1))/(-x^2)`
3. Simplify:
   `\displaystyle ((f)/(g))(x) = -(x^2 - x + 1)`