Question

If f: R -> R is defined by f(x) = 3x-4 prove that f is a bijection and find its inverse.​

Answer 1

A function which is one one (injective) and onto (surjective) is called bijective

Given :-

F : R -> R , F(x) = 3x - 4

Let , x1 and x2 are two different number and

F(x1) = F(x2)

Thus ,

3(x1) - 4 = 3(x2) - 4

3(x1) = 3(x2)

x1 = x2

Therefore , the function is one one

For every value of y there is x in set A i.e for every element of set (B) has pre image in set (A)

Therefore , the function is onto

Hence , the function is bijective

Let , y = 3x - 4

3x = 4 + y

x = (4 + y)/3

Therefore , the inverse is x = (4 + y)/3