Question

find the inverse of f informally. verify that f(f^-1(x))=x and f^-1(f(x))=x

f(x)= (x-1)/5

Answer 1

f(x)= (x-1)/5 ..............(1) let f(x)=y means x=f^-1(y)
y= (x-1)/5
x=5y+1 hence f^-1(y) = 5y+1
replace y by x f^-1(x) = 5x+1...................(2)

now from (1)and(2)
f(f^-1(x))=f(5x+1)=(5x+1-1)/5 =x hence f(f^-1(x))=x

f^-1(f(x)=f^-1((x-1)/5)=5{(x-1)/5}+1=x-1+1=x hence f^-1(f(x))=x

Answer 2

Any form of function when mapping it's own inverse function maps the object back to itself.

Answer 3

For that function:
\[f^{-1}(x)=5x+1\]:)
Do you need the steps?

Answer 4

no friend ...because problem says to do that..thats why i have chosed long path.