Mark (√) against the correct answer in the following: f : R + → R

1.	Mark (√) against the correct answer in the following: f : R + → R+ : f(x) = ex is A. many - one and into B. many - one and onto C. one - one and into D. one - one and onto
Answer» Correct Answer is (D) one - one and onto f(x) = e^x Since the function f(x) is monotonically increasing from the domain R⁺→ R⁺ ∴f(x) is one –one Range of f(x) = (1,∞) = R⁺ (codomain) ∴f(x) is onto ∴ f : R⁺ → R⁺ : f(x) = e^x is one - one onto.

Mark (√) against the correct answer in the following: f : R + → R+ : f(x) = ex is A. many - one and into B. many - one and onto C. one - one and into D. one - one and onto

Answer»

Correct Answer is (D) one - one and onto

f(x) = e^x

Since the function f(x) is monotonically increasing from the domain R⁺→ R⁺

∴f(x) is one –one

Range of f(x) = (1,∞) = R⁺ (codomain)

∴f(x) is onto

∴ f : R⁺ → R⁺ : f(x) = e^x is one - one onto.