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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.

Verified Answer :

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.

frika

Consider the funcion \(y=\sqrt{x}\). 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 \(y=\sqrt{7-x}\) 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.

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