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Domain of Derivative
- Thread starter Jason76
- Start date
Be more precise with your words.\(\displaystyle f(x) = \dfrac{1}{4}x - \dfrac{1}{6}\)
\(\displaystyle f'(x) = \dfrac{1}{4}\)
The derivative of the function is \(\displaystyle (-\infty, \infty)\)
What is the domain of the derivative?
The domain of \(\displaystyle x\) is \(\displaystyle (-\infty, \infty)\)
The range of \(\displaystyle f(x)\) is \(\displaystyle (-\infty, \infty)\)
The range of the derivative \(\displaystyle f'(x)\) is 1/4
Be more precise with your words.
The domain of \(\displaystyle x\) is \(\displaystyle (-\infty, \infty)\)
The range of \(\displaystyle f(x)\) is \(\displaystyle (-\infty, \infty)\)
The range of the derivative \(\displaystyle f'(x)\) is 1/4
Post edited.
But it didn't ask for the range of the derivative. Though, useful to know anyways.
HallsofIvy
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Do you understand what "domain" means?
Do you understand what "domain" means?
Domain is the values that x can go into, while range are the values in which y can come out.
The online homework asks for the domain. I guess some problem with it. I will check.
Are there any values of x for which f'(x) is not defined?Post Edited
\(\displaystyle f(x) = \dfrac{1}{4}x - \dfrac{1}{6}\)
\(\displaystyle f'(x) = \dfrac{1}{4}\)
The domain of the function is \(\displaystyle (-\infty, \infty)\)
What is the domain of the derivative?
Be more precise with your words.
The domain of > > \(\displaystyle x\) << is \(\displaystyle (-\infty, \infty)\)
The range of \(\displaystyle f(x)\) is \(\displaystyle (-\infty, \infty)\)
The range of the derivative \(\displaystyle f'(x)\) is 1/4
DrPhil, the domain of f(x), not x, is \(\displaystyle \ (-\infty, \infty).\)
Jason,
Domain is defined as all real values x can take such that the values the function, f(x), or expression (involving x) takes are real.
In simple terms:
Domain = real values that go into a function or expression
Range = real values that come out of the function or expression
When the function is y=1/4, the domain is all real numbers. Any real input value produces a real y value. The y value is the same for every x value. The range is 1/4.
When the expression is x=c, where c is a constant, the domain is c. The range is all real numbers. x=c, a vertical line, is not a function.
Domain is defined as all real values x can take such that the values the function, f(x), or expression (involving x) takes are real.
In simple terms:
Domain = real values that go into a function or expression
Range = real values that come out of the function or expression
When the function is y=1/4, the domain is all real numbers. Any real input value produces a real y value. The y value is the same for every x value. The range is 1/4.
When the expression is x=c, where c is a constant, the domain is c. The range is all real numbers. x=c, a vertical line, is not a function.
Last edited:
HallsofIvy
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The domain of both f(x) and x is \(\displaystyle (-\infty, \infty)\)!DrPhil, the domain of f(x), not x, is \(\displaystyle \ (-\infty, \infty).\)
Domain and range is all real numbers for original problem. But it asks about the domain of the derivative. Perhaps as someone said, I have to see for what values is \(\displaystyle f'(x)\) is undefined. But there are no such values, that I see.
The domain of both f(x) and x is \(\displaystyle (-\infty, \infty)\)!
I state it as: \(\displaystyle "The \ \ domain \ \ of \ \ f(x) \ \ is \ \ (-\infty, \infty), \ \ and \ \ the \ \ range \ \ of \ \ f(x) \ \ is \ \ (also) \ \ (-\infty, \infty)."\)
I am speaking of the domain and range of the function. \(\displaystyle \ \ \)The "domain of a function" consists of (already takes into account)
the extent of the acceptable x-values.
Someone would not correctly phrase one of those expressions as "the domain of x."
HallsofIvy
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Having already said "there are no values of x for which f'(x) is undefined" why would you need "online homework" to tell that the domain is "all real numbers".
There are some things you need to be careful about. Technically the domain of a function is part of its definition. If I say "f(x) is defined as (1/4)x+ 3 for \(\displaystyle 0\le x\le 1\)", then the domain of that function is the "closed interval from 0 to 1" or \(\displaystyle 0\le x\le 1\). Similarly, the domain of f'(x) is \(\displaystyle 0\le x\le 1\). Since f is NOT DEFINED for x< 0 or x> 1, neither is its derivative.
There are some things you need to be careful about. Technically the domain of a function is part of its definition. If I say "f(x) is defined as (1/4)x+ 3 for \(\displaystyle 0\le x\le 1\)", then the domain of that function is the "closed interval from 0 to 1" or \(\displaystyle 0\le x\le 1\). Similarly, the domain of f'(x) is \(\displaystyle 0\le x\le 1\). Since f is NOT DEFINED for x< 0 or x> 1, neither is its derivative.