How do you find domain and range for # f(x) =sqrt(4-3x) + 2#?

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Answer 1 · 2018-07-05T03:21:34

Domain: #(-oo,4/3]#

Range: #[2,oo)#

Let's start with the domain:

We know whatever we have under the radical cannot be negative, so we can set the following inequality:

#4-3x>=0#

Adding #3x# to both sides gives us

#3x<=4#

#x<=4/3# as our domain or #(-oo,4/3]# in interval notation.

What about the range?

The lowest value that this expression can take on is #2#, when the radical just evaluates to zero. Our range can be #2# or greater.

#[2,oo)# in interval notation

Hope this helps!