SOLUTION: State the domain of the following:
f(x)= square root (x-8)
Algebra.Com
Question 115346: State the domain of the following:
f(x)= square root (x-8)
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
You are asked to find the domain of x for the function
.
In order to get a real answer to the square root of a quantity, that quantity must have a
positive value ... including zero. How can you take the square root of a negative number and
get a real number as the answer? You can't because a real number multiplied by itself
only results in a positive number. For example, if you were asked to find the square root
of +9, the answer can only be +3 (because +3 times +3 = +9) or it can be -3 (because -3
times -3 = +9). So if you were asked to find the square root of -9 you can't because
neither squaring +3 nor squaring -3 will get you -9.
.
So the conclusion is that in this problem the quantity under the radical sign must be
positive which means that it must be greater than or equal to zero. In equation form this
can be written as the inequality:
.
.
Solve this inequality by adding +8 to both sides to get rid of the -8 on the left side
and the result is:
.
.
This means that the domain of x is limited to all real values of x that are greater than
or equal to +8 ... all the way toward positive infinity. Another way of expressing this
in algebraic form is:
.
.
where represents positive infinity.
.
Hope this helps you to understand the problem a little better.
.
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