Question

3. Find the inverse of the following, where f:R → R is defined as
(i) x-7
(ii) 1-9x
(iii) x+1/x-1 , x not equal to 1
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Answer 1

x-7=y

or,x=7+y

or,f^-1(y)=7+y

or,f^-1(t)=7+t

1-9x=y

or,9x=1-y

or,x=1-y/9

or,f^-1(t)=(1-t)/9

y=x+1/x-1

or,x+1=y(x-1)

or,x=1+y/(y-1)

f^-1(t)=1+t/t-1 where t is without 1