# How do you find the domain and range of 1/sqrt(8-t)?

Dec 1, 2017

Domain: All $x$ values$< 8$; $\setminus \quad \left[\setminus \infty , 8\right)$

Range: All $y$ values$> 0$; $\setminus \quad \left(0 , \setminus \infty\right]$

#### Explanation:

The domain is simply the values $x$, or in this case $t$, can have that will make the function defined.

For the above function, dividing by $0$ will be undefined, so $t \setminus \ne 8$.

We can express that in interval notation as $\left[\setminus \infty , 8\right)$, which means the domain is all values of $t$ less than $8$.

As for the range, we can plot the graph and find it from that.

We can see the graph starts just above $0$, and continues toward $\setminus \infty$ upward.

So we can express the range as $\left(0 , \setminus \infty\right]$, meaning all $y > 0$.