Question

For what values of x is the expression below defined?A.-5 x < 1B.5 > x -1C.5 > x > 1D.5 x 1

Answer 1

Given:

There are given that the expression:

`(√(x+5))/(√(1-x))`

Explanation;

First, let's notice that we need positives to numbers inside both roots.

So,

The root of a negative number is a math error.

Then,

With that information, let us analyze the options.

From option A:

If we add 5 to this inequality, we have:

`\begin{gathered} -5+5\leq x+5<1+5 \\ 0\leq x+5<6 \end{gathered}`

That means the number in the first root is positive.

Now, we want 1-x to be positive:

`\begin{gathered} -5\leq x<1 \\ 5\ge-x>-1 \\ 1+5\ge1-x>1-1 \\ 6\ge1-x>0 \end{gathered}`

So, it is positive:

Final answer;

Hence, the correct option is A.