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.