Exams › JEE Main › Maths

Which of the following functions is one-one?

1. f: (0, ∞) → R, f(x) = x² - 4x + 3
2. f: [0, ∞) → R, f(x) = x² + 4x - 5
3. f: R → R, f(x) = e^x + 1/e^x
4. f: R → R, f(x) = ln(x² + x + 1)

Correct answer: f: [0, ∞) → R, f(x) = x² + 4x - 5

Solution

On [0,inf) the function f(x)=x^2+4x-5 has derivative 2x+4>0, so it is strictly increasing and hence one-one. The other options each fail: x^2-4x+3 has its vertex at x=2 inside (0,inf); e^x+e^-x is even; ln(x^2+x+1) has its minimum at x=-1/2, all making them many-one.

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 →