Question

If the domain of the square root function f(x) is x<=7, which statement must be true?

7 is subtracted from the x-term inside the radical.
The radical is multiplied by a negative number.
7 is added to the radical term.
The x-term inside the radical has a negative coefficient.

Answer 1

Correct answer is D.

The expression inside the radical must be greater than or equal to zero.


`x \leq 7 \\0 \leq 7-x \\7-x \geq 0`

Therefore, the x-term inside the radical has a negative coefficient.

Answer 2

Consider the funcion
`y=√(x)`. The dmain of this function is
`\ge 0` and the range is
`y\ge 0`.

Now if
`x\le 7` you can calculate that

`x-7\le 0,\\ 7-x\ge 0`

and the function
`y=√(7-x)` will have the domain
`x\le 7` (state this using that expression under the root is
`\ge 0`).

As you can see the x-term inside the radical has a negative coefficient.

Answer: correct choice is D.