# What is the domain and range of f(x)= sqrt(x-4) + 2?

Oct 29, 2015

The domain is: $x \ge 4$
The range is: $y \ge 2$

#### Explanation:

The domain is all the x values where a function is defined. In this case the given function is defined as long as the value under the square root sign is greater than or equal to zero, thus:
$f \left(x\right) = \sqrt{x - 4} + 2$
The domain:
$x - 4 \ge 0$
$x \ge 4$
In interval form:
$\left[4 , \infty\right)$
The range is the all the values of a function within its valid domain, in this case the minimum value for x is 4 which makes the square root part zero, thus:
The range:
$y \ge 2$
In interval form:
$\left[2 , \infty\right)$