Exams › JEE Main › Maths

Given that f(x) = (x−1)/(x+1), what is the value of f(2x)?

1. (f(x)+1)/(f(x)+3)
2. (3f(x)+1)/(f(x)+3)
3. (f(x)+3)/(f(x)+1)
4. (f(x)+3)/(3f(x)+1)

Correct answer: (3f(x)+1)/(f(x)+3)

Solution

Let y = f(x) = (x-1)/(x+1), so x = (1+y)/(1-y). Then f(2x) = (2x-1)/(2x+1). Substituting and simplifying gives f(2x) = (3y+1)/(y+3) = (3f(x)+1)/(f(x)+3).

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 →