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Question 504141: How do I solve for the domain of f(x): 3x^4-10 algebraically?
Answer by tinbar(133)   (Show Source):
You can put this solution on YOUR website! A domain is simply a set of numbers which make sense for some given function.
In this particular example, all numbers work, since we can take any number, raise it to the power of 4, multiply it by 3 and subtract 10 from it. So you would say the domain is the set of Real numbers.
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You may now be wondering, is there any function for which the domain is not all numbers? It seems we should be able to do whatever we want with numbers. This is, however, not the case. Consider g(x) = 1/x. Is the domain all numbers? No, it is not, the number 0 fails. 1/0 is not defined mathematically, in other words, it makes no sense to try and do this. To see why this is let's say 1/0 is some number and we'll call it z. If 1/0=z, then by rearrangement 1=z*0, but 0 times anything is 0, so no matter what z is 0*z=0 not 1, so therefore this makes so sense. For g(x) then, we'd say the domain is all the numbers EXCEPT 0.
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