#### mathdad

##### Full Member

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- Apr 24, 2015

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Find domain of H(x) = (3x^2 + x)/(x^2 + 4).

Solution:

I understand the domain of a function defines the values of x that we can put into the function in order to get a valid output.

With rational functions,the textbook explains that we are concerned with the denominator, as the value of this cannot be zero.

Example:

For H(x) = f(x)/g(x), g(x) cannot be zero because division by zero is undefined.

Hence, the values of x NOT in the domain is defined when:

x^2+ 4 = 0

x^2 = - 4

This tells me that there are no real values that satisfy this condition.

The book's answer is

"The domain of H(x) is all real values of x with no restriction."

I do not understand the textbook's answer.

There are no real values that satisfy this condition for the function given but at the same time, the domain is all real numbers. Please, explain, in simple terms, the textbook definition....

Solution:

I understand the domain of a function defines the values of x that we can put into the function in order to get a valid output.

With rational functions,the textbook explains that we are concerned with the denominator, as the value of this cannot be zero.

Example:

For H(x) = f(x)/g(x), g(x) cannot be zero because division by zero is undefined.

Hence, the values of x NOT in the domain is defined when:

x^2+ 4 = 0

x^2 = - 4

This tells me that there are no real values that satisfy this condition.

The book's answer is

"The domain of H(x) is all real values of x with no restriction."

I do not understand the textbook's answer.

There are no real values that satisfy this condition for the function given but at the same time, the domain is all real numbers. Please, explain, in simple terms, the textbook definition....

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