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Find the domain of the definition of the functiony = [(x – 3)/(x + 3)]1/2 + [(1 – x)/(1 + x)]1/2.
- a)x > 3
- b)x < –3
- c)-3 £ x £ 3
- d)Nowhere
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Find the domain of the definition of the functiony = [(x – 3)/(x...
Both the brackets should be non-negative and neither (x + 3) nor (1+ x) should be 0.
For (x – 3)/(x + 3) to be non negative we have x>3 or x< – 3.
Also for (1– x)/(1+ x) to be non-negative –1 < x < 1. Since there is no interference in the two
ranges, Option (d) would be correct.
For (x – 3)/(x + 3) to be non negative we have x>3 or x< – 3.
Also for (1– x)/(1+ x) to be non-negative –1 < x < 1. Since there is no interference in the two
ranges, Option (d) would be correct.
Most Upvoted Answer
Find the domain of the definition of the functiony = [(x – 3)/(x...
Explanation:
The given function y = [(x - 3)/(x + 3)]^(1/2) * [(1 - x)/(1 + x)]^(1/2) involves square roots of fractions. For real numbers, the square root of a negative number is undefined.
Domain of the Function:
- To find the domain of the function, we need to consider the values of x that make the square roots of the fractions real numbers.
- The square root of a fraction is real only when the numerator is greater than or equal to 0 and the denominator is not equal to 0.
- In this case, the fractions inside the square roots are (x - 3)/(x + 3) and (1 - x)/(1 + x).
- For the first fraction to have a real square root, x should be greater than or equal to 3.
- For the second fraction to have a real square root, x should be less than or equal to 1.
- However, these conditions cannot be simultaneously satisfied, as x cannot be both greater than or equal to 3 and less than or equal to 1 at the same time.
- Therefore, there is no value of x that satisfies both conditions, and the function is undefined for all real numbers.
Conclusion:
The domain of the given function y = [(x - 3)/(x + 3)]^(1/2) * [(1 - x)/(1 + x)]^(1/2) is nowhere, as there is no value of x for which the function is defined.
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Find the domain of the definition of the functiony = [(x – 3)/(x + 3)]1/2 + [(1 – x)/(1 + x)]1/2.a)x > 3b)x < –3c)-3 £ x £ 3d)NowhereCorrect answer is option 'D'. Can you explain this answer?
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