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Question

The inverse of the function y=e2xe2xe2x+e2x is

A
loge(1+2x12x)
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B
14loge(1x1+x)
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C
14loge(1+x1x)
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D
an odd function
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Solution

The correct options are
B 14loge(1+x1x)
D an odd function
y=t1tt+1t where t=e2x
y(t2+1)=t21
t2=1+y1y
(e2x)2=1+y1y(t=e2x)
e4x=1+y1y
4x=loge(1+y1y)
x=14loge(1+y1y)
f1(x)=14loge(1+x1x)=p(x)
p(x)=p(x)
f1(x)=f1(x)
Thus f1(x) is an odd function.

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