Which of the following is true of f(x) = – 1 ⁄ √(x – 5) ?

Question

Accepted Answer

The square root of a negative value is imaginary, so the value of x – 5 cannot be negative. Since the square root is the denominator of a fraction, it cannot be equal to 0 either. The value of x – 5 must be greater than 0; x – 5 > 0, x > 5. The domain of f(x) is all real numbers greater than 5. Since the denominator of the fraction must always be positive, and the numerator of the fraction is –1, the value of f(x) will always be negative. No value of x will make f(x) = 0, so the range of f(x) is all real numbers less than 0.

Want a deeper, personalized explanation?

Related questions