Question

For what values of x is the expression below defined?x+5+ v1 -O A. 5 >x>1B. 5 sxs1C. -5 s x < 1D. 5 > XS-1SUBMIT

Answer 1

The correct range of definition is;

`C;\text{ -5}\leq x<1`

Here, we want to get the range of values of x for which the given expression is defined

The key here is that any value of x that will make us have a negative value inside the root will make the expression undefined as that would give us a non-real root

Now, let us take a look at the options;

a) if x is greater than 1, we will have a negative root on the right, making the expression undefined. This option is wrong

b) This is also wrong; if 5 is less than x, then x might be 6 , which would give a negative root value

c) If -5 is less than x, x could take values of -4, -3, -2 and the root on the right will never be negative. But in cases like this, we have the spectrum upto positive values of x such as 5 which would make the root on the right negative and undefined. This range here is the correct answer

d) Here, 5 is greater than x, so the root on the left can never be negative. For values less than -1, like -6, what we have on the left will be undefined