Given the following functions, perform the indicated operation and state the domain.
f(x) * g(x)
3X^1/2*6X^1/3. I got 18X^5/6. But without using a calculator how do i find the domain?????? Thanks:)
i don't understand. Can you please explain in simplier terms, thanks:)
If x is negative, then x^(1/2) is imaginary. (by the way x to the one third has two complex roots for negative x)
That kind of restricts the whole deal to positive real x.
you can not take the square root of a negative number, so x may not be negative
there is no negative number though
There is no negative X in the domain, exactly. The domain is all POSITIVE real X
To determine the domain of a function, we need to consider any restrictions on the values that the independent variable, in this case, x, can take.
In the given expression, we have f(x) * g(x), where f(x) = 3x^(1/2) and g(x) = 6x^(1/3).
To find the domain, we need to consider any values of x that would result in an undefined operation. In this case, we need to check if there are any values of x that would make either f(x) or g(x) undefined.
Since both f(x) = 3x^(1/2) and g(x) = 6x^(1/3) involve taking roots, we need to ensure that the radicand (the expression inside the root) in both functions is non-negative.
For f(x), the radicand is x^(1/2), which is the square root. The square root is defined for all non-negative real numbers. Therefore, the radicand must be greater than or equal to zero: x^(1/2) ≥ 0.
For g(x), the radicand is x^(1/3), which is the cube root. The cube root is defined for all real numbers, positive, negative, or zero. Therefore, there are no restrictions on the radicand.
Since the radicand for g(x) has no restrictions, we only need to consider the radicand for f(x).
So, the domain for the expression f(x) * g(x) is the set of all real numbers x such that x^(1/2) ≥ 0.
Since the square root is always non-negative, the domain for f(x) * g(x) is all real numbers.