Exams › JEE Main › Maths

Find the set of all real x for which the function f(x)=exp(√(5x-3-2x²)) is defined.

1. [3/2,∞)
2. [1,3/2]
3. (-∞,1]
4. (1,3/2)

Correct answer: [1,3/2]

Solution

The function f(x) is defined when the expression inside the square root, 5x - 3 - 2x², is non-negative. Solving the inequality leads to the interval [1, 3/2], where the function is valid.

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 →