Question

Let \[ f(x)=\sqrt{7-x} \] and \[ g(x)=\sqrt{x-5}. \] Then the domain of the function \[ h(x)=f(x)g(x) \] is:

• A. [5, 7]
• B. \((-\infty, 7]\)
• C. [5, \(\infty\))
• D. [-7, -5]
• E. \((-\infty, \infty)\)

Hint:

Whenever you see a product of multiple square roots, list all conditions \(radicand \geq 0\) and find the overlapping region on a number line. If the region is empty, the function is never defined.

Answer 1

The Correct Option is A