If f(x) = (4x + 3) / (6x - 4), x ≠ 2/3 , show that fof(x) = x, for all x ≠ 2/3. What is the inverse of f ?

Solution:

A function is a process or a relation that associates each element 'a' of a non-empty set A, to a single element 'b' of another non-empty set B.

The inverse of a function f(x) is a function g(x) such that if f maps an element ′a′ to an element ′b′, g maps ′b′ to ′a′.

According to the given problem,

(fof)(x) = f (f (x))

= f [(4x + 3)/(6x - 4)]

= 4 [(4x + 3)/(6x - 4)]/6 [(4x + 3)/(6x - 4)]

= (16x + 12 + 18x - 12)/(24x + 18 - 24x + 16)

= 34x/34 = x

Therefore,

fof (x) = x for all x ≠ 2/3 

Calculating inverse of f(x)

f(x) = (4x - 3) / (6x - 4),

put f(x) = y

y = (4x - 3) / (6x - 4)

On further simplifying we get, 

x = (4y - 3) / (6y - 4)

Hence, the given function f is invertible and the inverse of f is f itself

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NCERT Solutions for Class 12 Maths - Chapter 1 Exercise 1.3 Question 4

If f(x) = (4x - 3) / (6x - 4), x ≠ 2/3 , show that fof(x) = x, for all x ≠ 2/3. What is the inverse of f ?

Summary:

For the given function f(x) = (4x - 3) / (6x - 4), x ≠ 2/3, fof(x) = x and function f is invertible and the inverse of f is f itself