Question

Which statement is true about the function

Answer 1

Answer:

Option A is the answer.

Step-by-step explanation:

Given function is f(x) = -$\sqrt{-x}$

Option A. Domain of the function is all negative real numbers.

As we know under root of any negative number is not defined so this function is defined only for the values of x ≤ 0

Example : f(1) = -√(-1) Not defined

and f(-1) = -√-(-1) = √1 Defined

Therefore, domain of the function will be all negative real numbers.

Option B. Range of the function is all positive real numbers.

Example: f(-1) = -√-(-1) = -√1

                      = - 1

For x = -1, range of the function is negative.

Therefore, this option is not true.

Option C. Domain and Range of the function have opposite signs.

As we have seen in option B.

f(-1) = - 1

Therefore, domain and range of the function are of same sign. So this option is incorrect.

Option D. Domain and range of the function are same.

Example: f(-2) = -√-(-2) = -√2

                       = - 1.414 ≠ (-2)

Therefore, Domain and range are not same which shows that this option is incorrect.

Option A will be the answer.

Answer 2

You solve for the domain by setting the radicand less than or equal to 0 and solving for x.  Dividing by a -x, we switch the sign so we have that the domain is less than or equal to 0, or all negative numbers.  We know that it breaks every law in math to have a negative radicand with an even index, so if the domain is all negative values of x, taking a negative of a negative gives us a positive.  The negative sign OUTSIDE the radical means you are flipping the graph upside down.  So instead of having a range of y is greater than or equal to 0 as does the parent graph, you have flipped it upside down so it heads more negative in regards to the range.  Therefore, the domain and the range both have the same sign, thee last choice from above.