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.

Correct answer is D.

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

[tex]x \leq 7 \\0 \leq 7-x \\7-x \geq 0[/tex]

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

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frika frika · Answer 2 · 2018-07-31T19:52:29+02:00

Consider the funcion [tex] y=\sqrt{x} [/tex]. The dmain of this function is [tex] \ge 0 [/tex] and the range is [tex] y\ge 0 [/tex].

Now if [tex] x\le 7 [/tex] you can calculate that

[tex] x-7\le 0,\\ 7-x\ge 0 [/tex]

and the function [tex] y=\sqrt{7-x} [/tex] will have the domain [tex] x\le 7 [/tex] (state this using that expression under the root is [tex] \ge 0 [/tex]).

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

Answer: correct choice is D.

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.

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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.