How do you find the domain of a function?
Posted on Mar 11, 2008 under domain news and reports | 7 Commentsf(x) = sqrt (6 – x)
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March 11th, 2008 at 7:19 am
By eliminating invalid x values.
For f(x) = √(6-x), x ≥ 6, otherwise you're taking the square root of a negative number.
March 11th, 2008 at 7:19 am
The domain of a function is the set of all valid inputs. So you think about what can't go in the function and then say everything but.
In the case of a square root, you can't take the square root of a negative number. So think about 6 – x is less than 0. So x would be greater than 6. So the domain is what can go in the fucntion, that is, evernthing less than or equal to 6.
In the case of a rational function, you can't have a zero denominator. So set the denomnator equal to zero and solve. Then the domain is everything except that.
March 11th, 2008 at 7:19 am
f(x) = sqrt(6-x)
Think of x as the input; then f(x) is the output.
Domain = what you are allowed to use as input.
Range = what values can be reached by the output.
When analyzing an equation to find its domain, you have to find impossible situations, for example:
dividing by zero.
square roots of negative numbers,
logarithms of zero or negative numbers,
etc.
The domain cannot contain any values for which the equation becomes impossible.
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