The given function f is onetoone Find f and give its domain

The given function f is one-to-one. Find f\' and give its domain and range. f(x) = 2 + 4^x f(x) = 10^x+3 - 10 f(x) = 1 + In(x - 2) f(x) = 5 + log_2 1/x

Solution

49) f(x)=1+ln(x-2)

domain of f(x) is (2,)

range of f(x) is (-,)

given f(x) is one-to-one

let f(x)=y

=> x=f^-1(y)

y=1+ln(x-2)

=>ln(x-2)=(y-1)

=>x-2=e^y-1

=>x=2+e^y-1

=>f^-1(y)=2+e^y-1

=>f^-1(x)=2+e^x-1

domain of f^-1(x) is (-,)

range of f^-1(x) is (2,)