True or False. The domain of every rational function is the set of all real numbers.

Nannie Mack

Nannie Mack

Answered question

2021-01-31

True or False. The domain of every rational function is the set of all real numbers.

Answer & Explanation

Alannej

Alannej

Skilled2021-02-01Added 104 answers

for example:
f(x)=1/x, the domain s not the set of all real numbers
RESULT:False
madeleinejames20

madeleinejames20

Skilled2023-06-17Added 165 answers

Answer:
False. The domain of every rational function is the set of all real numbers, except for the values of x that make the denominator zero.
Explanation:
A rational function is defined as a function of the form:
f(x)=p(x)q(x)
where p(x) and q(x) are polynomials and q(x)0.
The domain of a rational function is the set of all real numbers except the values of x for which the denominator q(x) is equal to zero. This is because dividing by zero is undefined in mathematics.
Hence, the domain of a rational function is:
Domain={x|q(x)0}
Therefore, the statement ''The domain of every rational function is the set of all real numbers'' is false. The domain consists of all real numbers except those that make the denominator zero.
Eliza Beth13

Eliza Beth13

Skilled2023-06-17Added 130 answers

True or False. The domain of every rational function is the set of all real numbers.
The correct answer is:
False.
The domain of a rational function is the set of all real numbers except for the values that make the denominator equal to zero.
Mr Solver

Mr Solver

Skilled2023-06-17Added 147 answers

To determine whether the statement ''The domain of every rational function is the set of all real numbers'' is true or false, let's first define a rational function. A rational function is defined as the quotient of two polynomials, where the denominator polynomial is not equal to zero.
Let's suppose we have a rational function f(x). The domain of f(x) consists of all the values of x for which the function is defined. In other words, it is the set of all real numbers that we can substitute into the rational function to obtain a valid output.
For a rational function, the only values that we need to exclude from the domain are those that make the denominator equal to zero. This is because division by zero is undefined in mathematics.
Thus, the domain of a rational function is the set of all real numbers except for the values of x that make the denominator equal to zero. We can express this using LaTeX markup as:
Domain of a rational function={x:denominator0}
Therefore, the statement ''The domain of every rational function is the set of all real numbers'' is false. The domain of a rational function excludes the values of x that make the denominator equal to zero.

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