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

Jun 25, 2018

$x \setminus \ge \frac{7}{2}$

#### Explanation:

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

In your case, the function $y = \sqrt{2 x - 7}$ 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 $2 x - 7 \setminus \ge 0$, which yields

$2 x - 7 \setminus \ge 0 \setminus \iff 2 x \setminus \ge 7 \setminus \iff x \setminus \ge \frac{7}{2}$

which is your domain.