Math, asked by vijayak2601, 5 months ago

If f(x)=
e^x+e^-x/2
then the inverse f(x) is

Answers

Answered by Anonymous
1

f(x)=

e

x

+e

−x

e

x

−e

−x

+2

Let f(x)=y

Then, y=

e

x

−e

−x

e

x

−e

−x

+2

y=

e

x

−e

−x

e

x

−e

−x

+2e

x

+2e

−x

⇒ye

x

+ye

−x

=3e

x

+e

−x

⇒ye

x

+

e

x

y

=3e

x

+

e

x

1

⇒y.e

2x

+y=3e

2x

+1

⇒y.e

2x

−3e

2x

=1−y

⇒e

2x

(y−3)=1−y

⇒e

2x

=

y−3

1−y

2x=log

e

(

y−3

1−y

)

∴x=

2

1

log

e

(

y−3

1−y

)

y=f(x)⇒x=f

−1

(y)

∴f

−1

(y)=

2

1

log

e

(

y−3

1−y

)

∴f

−1

(x)=

2

1

log

e

(

x−3

1−x

)

=

2

1

log

e

(3−x

x−1)

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