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

1 Answer
Walker P
Mar 16, 2016

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.

Related questions
See all questions in Domain and Range of a Function
Impact of this question
6198 views around the world
You can reuse this answer
Creative Commons License