Question

39-46 find the domain of the function.

45. \(F\left( p \right) = \sqrt {2 - \sqrt p } \)

Short answer

The domain of the function is \(\left( {0,4} \right)\).

Step-by-step solution

Domain of the function

Let \(D\) and \(E\) be the sets of real numbers. Set \(D\) is referred to as the domain of the function. The domain of the function is the set of all inputs for which the formula produces a real number output.

Determine the domain of the function

The function \(F\left( p \right) = \sqrt {2 - \sqrt p } \) is defined if \(p \ge 0\) and \(2 - \sqrt p \ge 0\). Then

\(2 - \sqrt p \ge 0\)

\(2 \ge \sqrt p \)

\(\sqrt p \le 2.\)