Given the function u(x) and v(x), the function operation (u/v)(x) is -x³ + x² - 1 .
<h3>What is the function of operation (u/v)(x)?</h3>
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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