Functions Question 41
Question: Which one of the following is a objective function on the set of real numbers
[Kerala (Engg.) 2002]
Options:
A) $ 2x-5 $
B) $ |x| $
C) $ x^{2} $
D) $ x^{2}+1 $
Show Answer
Answer:
Correct Answer: A
Solution:
$ |x| $ is not one-one; $ \underset{x\to \infty }{\mathop{\lim }}\frac{4x}{(\sqrt{x^{2}+8x+3}+\sqrt{x^{2}+4x+3}} $ is not one-one; $ x^{2}+1 $ is not one-one. But $ 2x-5 $ is one-one because $ f(x)=f(y)\Rightarrow 2x-5=2y-5\Rightarrow x=y $ Now $ f(x)=2x-5 $ is onto. \ $ f(x)=2x-5 $ is bijective.
BETA
