Exams › JEE Main › Maths

Find the domain of each function: (i) f(x) = 1/sqrt(x - |x|) (ii) f(x) = sqrt(|x| - x) (iii) f(x) = sqrt(x - |x|) (iv) f(x) = 1/sqrt(|x| - x)

1. (i) empty set; (ii) all real x; (iii) x >= 0; (iv) x < 0
2. (i) x > 0; (ii) x < 0; (iii) x > 0; (iv) x > 0
3. (i) all real x; (ii) empty set; (iii) all real x; (iv) all real x
4. (i) x < 0; (ii) x > 0; (iii) x < 0; (iv) x < 0

Correct answer: (i) empty set; (ii) all real x; (iii) x >= 0; (iv) x < 0

Solution

Evaluate x - |x| and |x| - x piecewise. For square roots the radicand must be non-negative; when the expression is also in a denominator it must be strictly positive.

Related JEE Main Maths questions

• Given f(x)=(x(x-p))/(q-p)+(x(x-q))/(p-q), where p≠ q, determine the value of f(p)+f(q).
• A real-valued function f(x) obeys the relation f(x-y)=f(x)f(y)-f(a-x)f(a+y), where a is a fixed constant, and f(0)=1. Then the value of f(2a-x) is
• The set of all real values of x for which the function f(x)=(3)/(4-x²)+log₁₀(x³-x) is defined is:
• A relation R is defined on the set of integers Z by the condition that (x,y) belongs to R exactly when x² + y² = 9. Which statement below is false?
• If f(x)=√(1+x²), then which of the following statements is true?
• For the function f(x)=√(x-√(1-x²)), what is its domain?

⚔️ Practice JEE Main Maths free + battle 1v1 →