Question

What is the domain and range of `f(x) =sqrt(-2x+5)`?

Answer 1

Domain: (`-oo,2.5`]
Range: [`0,oo`)

Explanation:

Square roots should never have a negative value under the radical, otherwise, the solution to the equation will have an imaginary component.

With this in mind, the domain of `x` should always cause the expression under the radical to be greater than 0 (i.e. not negative).

Mathematically,
`-2x+5>=0`
`-2x>=-5`
`(-2x)/(-2)<=(-5)/-2` Note: at this point, the `>=` changes to `<=`
`x<=2.5`

This can be expressed as `(-oo,2.5]`. Using a bracket instead of a parentheses implies that the value 2.5 is included in the domain.

The corresponding range can be determined by plugging in the values from the domain. In doing so, it becomes clear that the range is `[0,oo)`, again implying that 0 is included in the range.