Domain of Two Rational Expressions

Junior (College 3rd year) ・Mathematics ・MLA

Domain is a set of all possible values that can give valid values for a function. In other words, the values of the independent variable for which the value of dependent variable can be defined are collectively known as the domain of the function.

The denominator of a function cannot be zero because a zero denominator makes the value of the fraction undefined. From the elementary mathematics, it is known that any number when divided by zero gives an undefined result. In case of a function, the value of the independent variable for which the denominator becomes zero yields an undefined value of the fraction and is excluded from the domain of the function.

Domain of Two Rational Expressions:

Rational Expression # 01

Domain: It is obvious that for no value of ‘b’ (independent variable), the denominator can be zero, since the denominator is a constant that does not include the variable ‘b’. So, the domain of the function is set of all real values. In set notation, it can be written as Df = {b | b ∈ ℜ} or, simply, Df = ℜ.

Rational Expression # 02

Domain: To find the domain values, let us set the denominator to zero, which will give us the excluded values from the set of domain.

Here, 10x2 + 5x = 0; we can factor the denominator as follows:

Or, 5x (2x+1) = 0; let us set each of the factor to the zero.

Or, 5x = 0 or, 2x +1 = 0

Or, x = 0 or, x = – ½

Therefore, the domain set will include all real numbers except ‘0’ and ‘-½’ for which the denominator becomes zero and the range becomes undefined. In set notation, it can be written as: Df = {x | x ∈ ℜ, x ≠ 0, –½}

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