Functions Question 660
Question: Which of the following function is even function
[RPET 2000]
Options:
A) $ f(x)=\frac{a^{x}+1}{a^{x}-1} $
B) $ f(x)=x( \frac{a^{x}-1}{a^{x}+1} ) $
C) $ f(x)=\frac{a^{x}-{a^{-x}}}{a^{x}+{a^{-x}}} $
D) $ f(x)=\sin x $
Show Answer
Answer:
Correct Answer: B
Solution:
In , $ f(-x)=\frac{{a^{-x}}+1}{{a^{-x}}-1}=\frac{1+a^{x}}{1-a^{x}}=-\frac{a^{x}+1}{a^{x}-1}=-f(x) $ So, it is an odd function. In , $ f(-x)=(-x)\frac{{a^{-x}}-1}{{a^{-x}}+1}=-x\frac{1-a^{x}}{1+a^{x}}=x\frac{a^{x}-1}{a^{x}+1}=f(x) $ So, it is an even function. In , $ f(-x)=-\sin [ \log (x+\sqrt{1+x^{2}}) ] $ So, it is an odd function. In , $ f(-x)=\sin (-x)=-\sin x=-f(x) $ So, it is an odd function.
BETA
