**One-one f:**

Consider x_{1} and x_{2} ∈ dom (f)

We know that

f(x_{1}) = f(x_{2})

**It can be written as**

(4x_{1} + 3)/ (6x_{1} – 4) = (4x_{2} + 3)/ (6x_{2} – 4)

So we get

(4x_{1} + 3) (6x_{2} – 4) = (4x_{2} + 3) (6x_{1} – 4)

**On further calculation**

24 x_{1} x_{2} – 16x_{1} + 18 x_{2} – 12 = 24 x_{1} x_{2} – 16x_{2} + 18x_{1} – 12

We get

34 x_{1} = 34 x_{2 }where x_{1} = x_{2}

f is one-one

**Onto f:**

**Consider y ∈ co domain (f)**

We know that y = f(x)

y = (4x + 3)/ (6x – 4)

**On further calculation**

6xy – 4y = 4x + 3

So we get

6xy – 4x = 3 + 4y

It can be written as

x (6y – 4) = 3 + 4y

So x = (3 + 4y)/ (6y – 4) ∈ domain Ɐ y ∈ co-domain

**f is an onto function**

**Here, x = (3 + 4y)/ (6y – 4) where y ≠ 2/3**

We get

**f **^{-1} (y) = (3 + 4y)/ (6y – 4) where y ≠ 2/3