If f: R → R is a function such that f(x) = 10x + 3 then find f-1 ?

  1. x103
  2. x+103
  3. x310
  4. x+310

Answer (Detailed Solution Below)

Option 3 : x310
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Detailed Solution

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Concept:

  • Inverse Function:

Let f: A → B be one-one and onto (bijective) function. Then f-1 exists which is a function f-1: B → A, which maps each element b ∈ B with an element

a ∈ A such that f(a) = b is called the inverse function of f: A → B.

  • Methods to find inverse:

Let f : A → B be a bijective function.

Step – I Put f (x) = y

Step – II Solve the equation y = f (x) to obtain x in terms of y.

Interchange x and y to obtain the inverse of the given function f.

Calculation:

Given: f: R → R is a function such that f(x) = 10x + 3

As we can see that, the given function is a bijective function i.e f-1 exists.

Let y = f(x) = 10x + 3

⇒ x = y310

Hence, f-1 (x) = x310

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