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unless otherwise specified the domain will be all real numbers, since you can take the absolute value of anything
I agree with satellite's diagnosis.
the real truth is that you should specify the domain of the function when you define it, but if you don't it is assumed to be the largest set of numbers on which the function can act, so in this case anything
I need to show algebra for credit
sorry but there is no algebra to do here
There is no algebra to show.
math is not about algebra, math is about reasoning
ok how about 2x^3-5x+6
It is a polynomial. Those things exist for any input x which means its domain is all read numbers
polynomial domain is still all real numbers. you only have to worry about division by zero, or taking a even root of a negative number. both of those are not allowed, but most things are permitted
The instructions are to find the domain algebraically. You set the function =0 and solve. I am not sure how to do this on these problems.
again, no algebra to show
Are you sure it says find domain and not x-intercepts?
setting the function = 0 tells you where it is zero, not what the domain is
yes I am sure and I realize that this tells me the zero but it is what I have to do in order to get credit. Going through and stating only domain with no work gets me nothing. I have to find the zero.
Finding the zero is not equivalent to finding the domain
those are separate problems and are unrelated
I understand what you all are saying. I am saying I have to find the zero to get credit for work. Would it help if I asked you to show me how to find the zero for these?
You could say that |x| >=0 for all real numbers so the domain is all real numbers.
There is no zero for f(x)=|x|+1
because |x| can never = -1
\[|x|+1\geq 1\] so it is never zero
what about 2x^3-5x+6?
So we can try syntehtic division to find rational solutions but this does not guarantee there are rational solutions
Did you perhaps say domain when you meant range?
No, I need to find the zero
i be right back using synthetic division and trail and error and finding zeros I found one zero to be x=-2
\[2x^2-4x+3=0\] solving this equation will give you the other two zeros