Question

find the range of the function

f=e^x+e^-x/e^x-e^-x​

Answer 1

Answer:

f(x)={ex+exex−ex,ex+e−xex−e−x,x⩾0x<0}

⇒f(x)={0,e2x+1e2x−1,x⩾0x<0}

y=e2x+1e2x−1   ⇒e2x=1−yy+1

This if for x<0

i.e 2x<0 ⇒ e2x<1

⇒0<1−yy+1<1

⇒y∈(−1,0)∀x<0

⇒y∈(−1,0