Question

What is the domain and range of y=the square root of 2x-7? Thanks

Answer 1

`x \ge 7/2`

Explanation:

The domain is the set of values which you can feed as input to your function.

In your case, the function `y=sqrt(2x-7)` has some restriction: you can't give any number as input, since a square root only accepts non-negative numbers.

For example, if you choose `x=1`, you'd have `y=sqrt(-5)`, which you can't evaluate.

So, you must ask that `2x-7 \ge 0`, which yields

`2x-7 \ge 0 \iff 2x \ge 7 \iff x \ge 7/2`

which is your domain.