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When asked to find a domain you start by assuming that it is all real numbers. Then you look for x values that need to be excluded. There are certain expressions that cannot be allowed in Math and any value for x that creates such an expression must be excluded from the domain.
Some of the more common expressions that must be avoided:
Zero denominators (since division by zero is undefined)
Negative radicands of even-numbered roots. ("Radicand" is the name for the expression within a radical. Even-numbered roots are square (2nd) roots, 4th roots, 6th roots, etc.) These must be avoided because you can't raise any real number to an even power and get a negative result.
Invalid arguments or bases of logarithms. (Valid arguments are positive. Valid bases are positive but not 1.
Our function has no logarithms. It does have a denominator. But it is a 4. And no matter what value x has, the denominator will always be 4, never zero.
Our function does have an even-numbered root, a square root. So we must make sure that x would never have a value that would make the radicand negative. Instead of thinking that x can't make the radicand negative it is easier to that we want x to make the radicand positive or zero. So we write a mathemtical sentence that says the radicand, , is greater than or equal to zero:
Solving for x...
Adding 2:
Multiplying by 4:
These are the values we want x to be. This is the domain of F(x): All numbers greater than or equal to 8.
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