The function f is onetoone Find its inverse and graph the fu

The function f is one-to-one. Find its inverse and graph the function and its inverse. State the domain and range of inverse function f(x) = 3x - 2/x + 5

Solution

Solution

solve for f(x) = y = (3x-2)/(x-5)

y (x-5) =(3x-2)

xy -5y = 3x-2

xy-3x = 5y-2

x(y-3) = 5y-2

x = (5y-2)/(y-3)

substitute x= y

inverse of f(x) = (5x-2)/(x-3)

  Domain of (5x-2)/(x-3) =

function is undefined at x =3 therefore domain = (-,3)(3,)

similerly range of (5x-2)/(x-3) =   (-,5)(5,)

Answer