If f(x) = x4 − x3 + x2 and g(x) = −x2, where x ≠ 0, what is (f ⁄g)(x)?

a. x^2-x+1

b. x^2+x+1 <- this is wrong

c. -x^2+x+1

d. - x^2-x+1

In this question we have two polynomic functions, the function f(x) is a quartic equation and the function g(x) is a quadratic equation. The division between functions is a binary operator defined as:

(f / g) (x) = f(x) / g(x) (1)

If we know that f(x) = x⁴ - x³ + x² and g(x) = - x², then we obtain the expression for the division by algebraic handling:

(f / g) (x) = (x⁴ - x³ + x²) / (- x²)

(f / g) (x) = x⁴ / (- x²) - x³ / (- x²) + x² / (- x²)

(f / g) (x) = - x² + x - 1

The expression for the division of the two functions is equal to (f / g) (x) = - x² + x - 1. (Correct choice: C)

To learn more on functions: https://brainly.com/question/12431044

#SPJ1

If f(x) = x4 − x3 + x2 and g(x) = −x2, where x ≠ 0, what is (f ⁄g)(x)? a. x^2-x+1 b. x^2+x+1 <- this is wrong c. -x^2+x+1d. - x^2-x+1

Respuesta :

How to find the expression of the division of two functions

Otras preguntas

If f(x) = x4 − x3 + x2 and g(x) = −x2, where x ≠ 0, what is (f ⁄g)(x)?

a. x^2-x+1

b. x^2+x+1 <- this is wrong

c. -x^2+x+1

d. - x^2-x+1