GREhelp wrote:
Assume the function f(x) is defined as follows: \(f(x) = (x-4)^2 + \sqrt{(x+3)} + \frac{5}{x+2}\). For Which of the following values of x is f(x) defined?
Indicate all such values.
A. -5
B. -4
C. -3
D. -2
E. -1
The answer is C and E. I could only select one in the official answer choice box.
You should know two properties:
1. The square root from a negative number is not defined, thus x+3 must be more than or equal to 0: \(x+3 \geq 0\) --> \(x \geq-3\). Eliminate options A, and B.
2. Division by 0 is not allowed, thus x+2 cannot be 0, which means that x cannot be -2. Eliminate D.
Answers C and E.
Hope it's clear.