How do you find the domain and range of #f(x) = (x) / sqrt(x^2+x+1)#?
Domain: Range:
Take note of this:
Find the range by letting:
Next:
Taking both sides equal:
Thus:
along with
That is:
Thus:
additionally:
plot{x/sqrt(x^2+x+1) [-5, 5, -2.5, 2.5]}
By signing up, you agree to our Terms of Service and Privacy Policy
Domain: Range:
This approach makes use of some calculus and pre-calculus.
Take note of this:
We discover:
plot{x/sqrt(x^2+x+1) [-5, 5, -2.5, 2.5]}
By signing up, you agree to our Terms of Service and Privacy Policy
To find the domain of the function ( f(x) = \frac{x}{\sqrt{x^2+x+1}} ), we need to ensure that the expression under the square root, ( x^2+x+1 ), is positive. This is because the square root of a negative number is undefined in the real number system. Therefore, we need to solve the inequality ( x^2+x+1 > 0 ) to determine the values of ( x ) that are valid for the domain.
To find the range of the function, we need to consider the behavior of the function as ( x ) approaches positive and negative infinity. Additionally, since the function is continuous and the denominator is never zero, there are no vertical asymptotes. Therefore, the range of the function is all real numbers.
In summary:
- Domain: ( x^2+x+1 > 0 )
- Range: All real numbers
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7