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Question

The inverse of the function f(x)=exexex+ex is

A
12n1+x1x
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B
12n2+x2x
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C
12n1x1+x
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D
2n(1+x)
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Solution

The correct option is B 12n1+x1x
y=exexex+ex
y=e2x1exe2x+1ex
y=e2x1e2x+1
for universe replace;x with y
x1=e2y1e2y+1
using componendo divodendo
x+1x1=e2y1+e2y+1e2y1e2y1
x+1x1=2e2y2
1+x1x=e2y
(1+x1x)=2y
y=12ln(1+x1x)

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