Question

Which of the following is one-one function defined from R to R

(A) f(x) = |x|

(B) f(x) = cos x

(C) f(x) = e^x

(D) f(x) = x²

Answer 1

Answer is (C)

f(x) = e^x

Let x, y ∈ R are such that

f(x) = f(y)

⇒ e^x = e^y

⇒ x log_e e = y log_e e

⇒ x = y

f(x) = f(y)

⇒ x = y [∵ log_e e = 1]

f is one-one function ∀ x, y ∈ R