Question

If u(x) = x5 – x4 + x2 and v(x) = –x2, which expression is equivalent to (StartFraction u Over v EndFraction) (x)?

Answer 1

Given the function u(x) and v(x), the function operation (u/v)(x) is -x³ + x² - 1 .

What is the function of operation (u/v)(x)?

Given the functions in the question;

• u(x) = x⁵ - x⁴ + x²
• v(x) = -x²
• (u/v)(x) = ?

To determine (u/v)(x), we replace the function designators in u/v with the actual functions.

(u/v)(x) = (x⁵ - x⁴ + x²) / (-x² )

To simplify, we factor out the common factor.

(u/v)(x) = x²(x³ - x² + x⁰ ) / x²(-x⁰ )

Cancel out the common factors

(u/v)(x) = (x³ - x² + x⁰ ) / (-x⁰ )

(u/v)(x) = (x³ - x² + 1 ) / (-1 )

Move -1 from the denominator and apply distributive property.

(u/v)(x) = (-1)(x³ - x² + 1 )

(u/v)(x) = -x³ + x² - 1

Given the function u(x) and v(x), the function operation (u/v)(x) is -x³ + x² - 1 .

Learn more about composite function here: brainly.com/question/20379727

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