wiz-icon
MyQuestionIcon
MyQuestionIcon
2
You visited us 2 times! Enjoying our articles? Unlock Full Access!
Question

Let exexex+ex=ln1+x1x, then find x

Open in App
Solution


Consider f(x)=exexex+ex=e2x1e2x+1=12e2x+1
f(x)=4e2x(e2x+1)2>0,xR
f(x) is an increasing function.
Domain : R, Range :(1,1)
For f:R(1,1),
f(x)=exexex+ex,fx:(1,1)R
x=exexex+ex
ey=1+x1xf(x)=ln1+x1x.
Hence, given equation is equivalent to f(x)=f(x).
f(x)=x (as f is an increasing function)
ln1+x1x=x1+x1x=e2x
Now, draw the graph of y=1+x1x and y=e2x. They intersect each other at x=0.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Monotonicity
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon