Question

The largest set of real values of x for which $f\left(x\right)=\sqrt{(x+2)(5-x)}-\frac{1}{\sqrt{x^2-4}}$ is real is:

• A. (1,2) U (2,5)
• B. (2,5)
• C. (3,4)
• D. (5,8)

Answer 1

The correct option is B

(2,5)

For f(x) to be real, the least value x can take is something slightly greater than 2 so that the denominator does not go to zero. Also, the maximum value x can take is 5, because beyond that the first part of the expression will be an imaginary number.