Exams › JEE Main › Maths

Which of the following pairs of functions are identical (equal as functions)? Here [x] is the greatest integer function and {x} the fractional part. (i) f(x) = sgn(x² - 3x + 4) and g(x) = e^[{x}]; (ii) f(x) = sqrt((1 - cos 2x)/(1 + cos 2x)) and g(x) = tan x.

1. Only (i)
2. Only (ii)
3. Both (i) and (ii)
4. Neither (i) nor (ii)

Correct answer: Only (i)

Solution

Two functions are identical only if they have the same domain and the same output everywhere. The square-root expression introduces an absolute value, which breaks equality with tan x on intervals where tan x < 0.

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 →