Exams › JEE Main › Maths

Determine the domain of each function: (i) y = log10(sqrt(x - 4) + sqrt(8 - x)); (ii) y = log10[1 - log10(x² - 5x + 16)]. Which option gives the correct domains for (i) and (ii) respectively?

1. (i) [4, 8] (ii) (2, 3)
2. (i) (4, 8) (ii) [2, 3]
3. (i) [4, 8] (ii) [2, 3]
4. (i) (4, 8) (ii) (2, 3)

Correct answer: (i) [4, 8] (ii) (2, 3)

Solution

Part (i) needs both radicals defined and their sum positive. Part (ii) needs the inner log defined and the outer log's argument positive, which bounds the quadratic between 1 and 10.

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 →