Which of the following functions are odd functions

Question

Which of the following functions are odd functions (A) f(x)=x((ax+a-x/ax-a-x)) (B) f(x)=(ax+x/ax-x) (C) f(x)=(ax-1/ax+1) (D) f(x)=x log 2(x+√x2+1)

Tardigrade Admin · Accepted Answer

f(x)=x (ax+a-x/ax-a-x) ⇒ f(-x)=f(x) ⇒ f is not odd. f(x)=(ax+x/ax-x) ⇒ f(-x)=(1-x ax/1+x ax) ≠-f(x) ⇒ f is not odd f(x)=(ax-1/ax+1) ⇒ f(-x)=(1-ax/1+ax)=-f(x) ⇒ f is odd. f(x)=x log 2 √(x+√x2+1) ⇒ f(-x) =-x log (-x+√x2+1) ≠ f(-x)

Q. Which of the following functions are odd functions

$f (x) = x (\frac{a ^{x} + a ^{- x}}{a ^{x} - a ^{- x}})$

$f (x) = \frac{a ^{x} + x}{a ^{x} - x}$

$f (x) = \frac{a ^{x} - 1}{a ^{x} + 1}$

$f (x) = x lo g_{2} (x + x^{2} + 1)$

Q. Which of the following functions are odd functions

f(x)=x(ax−a−xax+a−x​)

f(x)=ax−xax+x​

f(x)=ax+1ax−1​

f(x)=xlog2​(x+x2+1​)

f(x)=xax−a−xax+a−x​⇒f(−x)=f(x)⇒f is not odd. f(x)=ax−xax+x​⇒f(−x)=1+xax1−xax​=−f(x) ⇒f is not odd f(x)=ax+1ax−1​⇒f(−x)=1+ax1−ax​=−f(x)⇒f is odd. f(x)=xlog2​(x+x2+1​)​⇒f(−x) =−xlog(−x+x2+1​)=f(−x)

$f (x) = x (\frac{a ^{x} + a ^{- x}}{a ^{x} - a ^{- x}})$

$f (x) = \frac{a ^{x} + x}{a ^{x} - x}$

$f (x) = \frac{a ^{x} - 1}{a ^{x} + 1}$

$f (x) = x lo g_{2} (x + x^{2} + 1)$