Question

Q. Find the domain of the function y=√(2-√x) .

Answer 1

Solution:

y=$\sqrt{\smash[b]{2-\sqrt{\smash[b]{x}}}}$

Since we have square root ,So the value under this cannot be negative.

It means 2-$\sqrt{\smash[b]{x}}$ ≥ 0  ------------- condition (1)

However at the same time we need to take care that $\sqrt{\smash[b]{x}}$  ≥ 0 ------------- condition (2)

So considering both the condition we can say x ≥ 0 and x ≤ 4

Let x=0

y = $\sqrt{\smash[b]{2-\sqrt{\smash[b]{0}}}}$ ⟹ valid number under square root

Let x=1

y = $\sqrt{\smash[b]{2-\sqrt{\smash[b]{1}}}}$ ⟹ valid number under square root

Let x=2

y = $\sqrt{\smash[b]{2-\sqrt{\smash[b]{2}}}}$ ⟹ valid number under square root

Let x=3

y = $\sqrt{\smash[b]{2-\sqrt{\smash[b]{3}}}}$ ⟹ valid number under square root

Let x= 4

y = $\sqrt{\smash[b]{2-\sqrt{\smash[b]{4}}}}$ ⟹ valid number under square root

Now Let x=5

y = $\sqrt{\smash[b]{2-\sqrt{\smash[b]{5}}}}$ ⟹ This gives a negative number under square root

From here(x ≥ 5) each and every value of x will give a negative value under square root

So Domain of function is [0,4]