Functions Question 17
Question: The function $ f:R\to R $ defined by $ f(x)=e^{x} $ is
[Karnataka CET 2002; UPSEAT 2002]
Options:
A) Onto
B) Many-one
C) One-one and into
D) Many one and onto
Show Answer
Answer:
Correct Answer: C
Solution:
Function $ f:R\to R $ is defined by $ f(x)=e^{x} $ . Let $ x_1,,x_2\in R $ and $ f(x_1)=f(x_2) $ or $ {e^{x_1}}={e^{x_2}} $ or $ x_1=x_2 $ . Therefore f is one-one. Let $ f(x)=e^{x}=y $ . Taking log on both sides, we get $ x=\log y $ . We know that negative real numbers have no pre-image or the function is not onto and zero is not the image of any real number. Therefore function f is into.
BETA
