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# Domain of a radical function

Video transcript

Find the domain
of f of x is equal to the principal square
root of 2x minus 8. So the domain of
a function is just the set of all of the possible
valid inputs into the function, or all of the possible
values for which the function is defined. And when we look at how the
function is defined, right over here, as the square root,
the principal square root of 2x minus 8, it's only
going to be defined when it's taking the
principal square root of a non-negative number. And so 2x minus
8, it's only going to be defined when 2x minus 8
is greater than or equal to 0. It can be 0, because then you
just take the square root of 0 is 0. It can be positive. But if this was negative,
then all of a sudden, this principle square root
function, which we're assuming is just the plain vanilla
one for real numbers, it would not be defined. So this function definition is
only defined when 2x minus 8 is greater than or equal to 0. And then we could
say if 2x minus 8 has to be greater
than or equal to 0, we can solve this
inequality to see what it's saying about
what x has to be. So if we add 8 to both
sides of this inequality, you get-- so let me just
add 8 to both sides. These 8's cancel out. You get 2x is greater
than or equal to 8. 0 plus 8 is 8. And then you divide
both sides by 2. Since 2 is a
positive number, you don't have to swap
the inequality. So you divide both sides by 2. And you get x needs to be
greater than or equal to 4. So the domain here is the
set of all real numbers that are greater than
or equal to 4. x has to be greater
than or equal to 4. Or another way of saying
it is this function is defined when x is
greater than or equal to 4. And we're done.