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

Apr 30, 2018

Dom $f \left(x\right) = \left\{x \in \mathbb{R} / x \ge 4\right\}$

Range or Image of $f \left(x\right) = \left[0 + \infty\right)$

Explanation:

The expresion under square root must be positive or zero (square roots of negative number are no reals numbers). So

$4 - x \ge 0$

$4 \ge x$

So the domain is the set of real numbers smaller or equal than 4

In interval form $\left(- \infty , 4\right]$ or in set form

Dom $f \left(x\right) = \left\{x \in \mathbb{R} / x \ge 4\right\}$

Range or Image of $f \left(x\right) = \left[0 + \infty\right)$