Sonalika42 wrote:

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

I am assuming you mean f(x) is a real valued function and we need to select all options where f(x) is a real number.

In the function there is a square root term, \(sqrt(x+3)\) and the term \(\frac{5}{(x+2)}\). That can yield non real values/ undefined values.

\(\frac{5}{(x+2)}\) is undefined for x=-2. For x= -2 \(\frac{5}{(x+2)}\) becomes \(\frac{5}{(-2+2)}\) or \(\frac{5}{0}\). Which is undefined.

\(sqrt(x+3)\) is not real is \(x+3 < 0\), or \(x< -3\).

So as long as x is greater than or equal to -3. and x is not equal to -2, \(f(x)\) is a real number.

Hence all the options A, B, C, D, E are valid.

PS: Could you please share the page number of his question.??

_________________

Sandy

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