Question

f:(0,1]→R defined by f(x)=e^1/x then find f is​

Answer 1

Answer:

f(x)=

1−bx

b−x

f

′

(x)=

(1−bx)

2

−(1−bx)+b(b−x)

=

(1−bx)

2

b

2

−1

<0 for 0<b<1

Therefore, f is always decreasing function and thus it is invertible

let f(x)=

1−bx

b−x

=y

⇒x=

1−by

b−y

Therefore, f

−1

(x)=

1−bx

b−x

=f(x)

and f

′

(b)=

b

2

−1

1

and f

′

(0)=b

2

−1