Raphael K. answered • 09/17/21
Engineer with 10+ years of tutoring math and science
Please help ?????????
Determine the domain of the function f(x)=x√x2−62. (Use symbolic notation and fractions where needed. Give your answer as a union of intervals of the form (*,*), listing them in the left to right x-coordinate order. Use appropriate type of parenthesis "(", ")", "[" or "]" depending on whether the interval is open or closed.) Domain =
You could graph this and look at how it works, or approach it algebraically looking for vertical and horizontal asymptotes.
Algebraically:
Because there is x's in the denominator, we got to be careful not to let the denominator = 0, because then it is undefined. SO set the bottom equal to 0 and solve to find which x values to not include in the domain...
But wait, there's more!!!
Not only is x in the denominator, but a radical is in the denominator too. Radicals can never be negative, so we know that we need to make sure the denominator is not only NEVER zero, but also NEVER negative.
Do this by setting denoiminator to greater than 0
...
√[x2-62] > 0 *to get the domain.
x2-62 > 0
x2 > 62
x = +/- √62
On a number line, test whether the statement is true when you plug x values between each solution into the following expression: √[x2-62] > 0
———- √62——————+ √62—————
Use -8, 0, and 8
√[(-8)2-62] > 0 True
√[(0)2-62] > 0 False
√[(8)2-62] > 0 True
The domain is limited to: x< - √62 or x> +√62
In interval notation this would be (-∞,- √62)U(+ √62, ∞)
