Question

Let A = R - {3} and B = R - {1}

Let f: A to B be defined by

f(x) = (x-2)/(x-3)

a)" "f is bijective

b)" "f is one-one

c)" "f is onto

d)" "one to one but not onto

Solution

To check wether f is one-one,

f(x) = f(y)

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

Solving this, x = y

Hence, f is one-one function

Now, (x-2)/(x-3) = y

=> x = (3y-2)/(y-1)

This shows that codomain of f belongs to range of f.

Hence, f is one-one, onto and bijective function.