Assume the function \(f(x)=(x−5)^2+ sqrt(x+3) + \frac{5}{(x+2)}\)


For which of the values f(x) is defined?
Indicate all possible values.
a. 6
b. 5
c. 4
d. 3
e. 2
f. 1

Answer is d and f

i dont understand the explaination


or f(x) to be defined, the individual terms of f(x) need to be real. The conditions are analysed below:

(x−5)^2 will be real regardless any value of x<
√x+3 will be defined if x≥−3 So, D, E , F are possible.
5/(x+2) will be defined if the denominator (x+2)≠0(. So x cannot be -2. So the only options remain are D and F.