Let
f(x) = 2x/(x^2+9).
Find the domain of f. Write your answer using interval notation.
since the denominator can never equal to zero and it contains no square roots or other strange operators,
domain : x ∊ R
I like the "old fashioned" format I used, I always have to look up this "interval notation stuff"
I will let you write it your way.
To find the domain of a function, we need to identify all the values of x for which the function is defined. In this case, the function f(x) is defined for all values of x except where the denominator, x^2+9, is equal to zero since division by zero is undefined.
To find the values of x where the denominator is zero, we need to solve the equation x^2 + 9 = 0. Subtracting 9 from both sides, we get x^2 = -9. Taking the square root of both sides, we have x = ±√(-9).
However, there is a problem here. The square root of a negative number is not a real number. Therefore, there are no real solutions to the equation x^2 + 9 = 0.
This means that the denominator x^2 + 9 is never equal to zero for any real value of x. Hence, there are no restrictions on the values of x. The function is defined for all real numbers.
Thus, the domain of f(x) is (-∞, ∞) in interval notation, which indicates that f is defined for any value of x.
To find the domain of the function f(x) = 2x / (x^2 + 9), we need to determine the values of x for which the function is defined.
The function f(x) is defined for all real numbers except where the denominator, x^2 + 9, is equal to zero. We need to find the values of x that make the denominator zero.
Setting x^2 + 9 equal to zero, we have:
x^2 + 9 = 0
Subtracting 9 from both sides, we get:
x^2 = -9
Taking the square root of both sides, we have:
x = ±√(-9)
Since taking the square root of a negative number results in an imaginary number, there are no real values of x that make the denominator zero. Therefore, the function f(x) = 2x / (x^2 + 9) is defined for all real numbers.
Hence, the domain of f(x) is (-∞, ∞).