SOLUTION: Beyond confused about interval notation.
Say I need to find the domain of: g(x)=√(x+7) - 1/x
So I know I need to set √(x+7)≥0 and then the denominator of -1
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-> SOLUTION: Beyond confused about interval notation.
Say I need to find the domain of: g(x)=√(x+7) - 1/x
So I know I need to set √(x+7)≥0 and then the denominator of -1
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Question 947436: Beyond confused about interval notation.
Say I need to find the domain of: g(x)=√(x+7) - 1/x
So I know I need to set √(x+7)≥0 and then the denominator of -1/x is x>0.
Therefore, the answers would be:
x≥-7 and x>0 ok I understand this far. But interval notation keeps confusing me.
Why is the answer suppose to be -7≤x<0
I know that x≥-7 is the same as -7≤x because for x to be greater than -7 therefore -7 must be ≤x I understand that so -7≤x makes sense but where does the x<0 come from? How can x>0 be the same as x<0 for the answer, How is x greater than zero the same as x less than zero?
Please help Answer by josgarithmetic(39630) (Show Source):
Critical values for x are 0 and -7. Your discussion focuses on the domain.
You found that the domain is the set of x values such that or . You want maybe those x values in interval notation. Why the domain as just stated?
The critical values of x split the x real number line into THREE intervals. The set of point which satisfy your function conforms to inequalities. The intervals on the x real number line for g(x) are:
Values less than -7;
values between -7 and 0;
values greater than 0.
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The intervals expressed as inequality symbolism in that same order, and according to what your function indicate: ; ; .
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The latter of these two intervals are the acceptable x values for your g(x).
Stay clear-headed about acceptable values of x for the function, and any one specific value of x. Domain means, the acceptable values of input for a function. Note that for your g(x), x must not be 0. As a symbolized inequality this is .
(