Question

Let the domain of the given function be all real numbers. Find all possible values for theconstant an(q) = Vq2 + a +3

Answer 1

`n(q)\text{ = }√((q^2)\text{ + a )+ 3}`

We need to find the values of "a" that result in the function being real. For that the number inside the square roots must be greater or equal to zero, therefore:

`q^2+a\text{ }\ge0`

We need to isolate the "a" variable on the left side now.

`a\text{ }\ge-q^2`

The value of "a" is anything greater or equal to -q².