Question

Find the domain and range of $f\left(x\right)=\sqrt{x-5}$

Answer 1

$f\left(x\right)=\sqrt{x-5}$

For $f\left(x\right)$ to be defined, the term under the Square-root should be greater than or equal to zero.

$x-5\ge 0$

$x\ge 5$

So, the domain is $[5,\infty )$

Now, for $x-5\ge 0$

$\sqrt{x-5}\ge 0$

$y\ge 0$

So, the range is $[0,\infty )$