Question

range of
$2 \sqrt{x - 1}$
​

Answer 1

Answer:

We have,

f(x)=(x−1)(3−x)

Now,

Under square root the polynomial must be positive. The domain is obtained by solving:-

(x−1)(3−x)≥0

You can obtain the zeroes of the polynomial

(x−1)(3−x)=0

If

x−1=0

x=1

If

3−x=0

⇒x=3

So,

x=1,3

So the polynomial is solved in the external intervals.

x>1,x>3

So,

x∈(1,+∞)

Since the function f(x) is positive, due to result of square root,

The range includes all positive real numbers x≥0

Hence, this is the answer.