Answer to Question #91578 in Trigonometry for Sajid

Question #91578
Q. Find the domain of the function y=√(2-√x) .
1
Expert's answer
2019-07-19T09:25:10-0400

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]

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Comments

Rupinder kaur
14.07.19, 11:40

The domain means the values of x which are acceptable. Here in the root only non negative values are acceptable. Thus 2-√x is greater than or equal to 0.this means 2 G. E √X. MEANS 4 G.E. X( squaring both sides) then this means x lies between 0 and 4.This is the domain

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