What is the domain of the function f(x) = 2x^2 - 3?
1 answer:
Domain: Set of all real numbers
If you want to express the domain in set-builder notation, then you'd write something like
which is fancy notation to basically say "x is any real number"
If you want to write the domain in interval notation, then you'd write
which is the interval from negative infinity to positive infinity. In other words, the entire real number line.
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The domain is the set of all real numbers because we don't have any restrictions to worry about. There are no division by zero errors. There are no cases where we have to worry about taking the square root of a negative number, or anything similar. Any number can replace x to generate an output for y.
If you want to express the domain in set-builder notation, then you'd write something like
If you want to write the domain in interval notation, then you'd write
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The domain is the set of all real numbers because we don't have any restrictions to worry about. There are no division by zero errors. There are no cases where we have to worry about taking the square root of a negative number, or anything similar. Any number can replace x to generate an output for y.
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The polynomial 
may have solutions which are the divisors of -20, therefore -20 has the following divisors: 
.
If x=1, then
,
if x=-1, then
,
if x=2, then
, then x=2 is a solution and you have the first factor (x-2).
If x=-2, then
, then x=-2 is a solution, so you have the second factor (x+2).
Since x-2 and x+2 are two factors of , then the polynomial 
is a divisor of and dividing the polynomial by you obtain
.
If x=1, then
if x=-1, then
if x=2, then
If x=-2, then
Since x-2 and x+2 are two factors of