Let f: R → R be the function defined by f (x) = 3x – 5 ∀ x ∈ R. Then write f –1.

  1. None of these

Answer (Detailed Solution Below)

Option 1 :
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Detailed Solution

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CONCEPT:

A function f: X → Y is defined to be invertible, if there exists a function g: Y → X such that g o f = Ix and

f o g = IY. The function g is called the inverse of f and is denoted by f –1.

  • For calculation of inverse of any function, it should be arranged in the terms of x = f(y) and then every y should be replaced with x.


CALCUATIONS:

Given that f (x) = 3x – 5 = y (say),

 then 3x = y + 5  ⇒  

Hence   ⇒ 

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