Question

647/4848

Answer 1

To find the real domain you can make use of the fact we cannot take square root of a negative number. In the first choice, x - b is inside the square root and so x - b > 0 or x > b. But the problem states the domain is [-b, infinity) and so this is not the correct choice. Try each choice and see which gives domain of [-b, infinity) which is same as saying x \(\ge\) -b.

Answer 2

I don't really know how to do it but I tried...is it c?

Answer 3

In a) and c) we are taking the cube root. There is no restriction in taking the cube root as a cube root is defined for ALL negative and positive values as well as zero. So there is no restriction on the domain when taking cube root.

In b) and d) we are taking square root. Square root has the restriction that you cannot take square root of a negative number.

Answer 4

\[
d) f(x) = -\sqrt{x+b} - a \\
\text{We cannot take square root of a negative number. Therefore, } \\
x + b \ge 0 \\
x \ge -b \\
\text{Domain :} [-b, \infty]
\]

Answer 5

\[
\text{Domain: }[-b, \infty)
\]

Answer 6

Only the last function, d), has the given domain.