Give an example of a function, f(x), with a domain of (0,5] and a range of [0,∞).
I've came up with the following. Is there a way to change it to limit domain to the (0,5]?
|(1/x) + ((1/x) - 5))|
sqrt(5-x)/x
To create a function with a domain of (0,5], you can modify your initial expression as follows:
Start with the function:
f(x) = |(1/x) + ((1/x) - 5)|
To restrict the domain to (0,5], you'll need to make sure that the function is only defined within that range. You can do that by using a piecewise function, which will have different expressions for different intervals.
For x values less than or equal to 0 or greater than 5, the function can be undefined or equal to some specific value (it doesn't matter as long as it's outside the desired range).
So, let's define the function piecewise:
For x ≤ 0 or x > 5:
f(x) = undefined (or any value outside the range [0, ∞))
For 0 < x ≤ 5:
f(x) = |(1/x) + ((1/x) - 5)|
This modified function with a limited domain of (0,5] retains the original range of [0, ∞).