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KCET2012MathematicsFunctions

If f: R R is defined by f(x)=2 x+3 , then f ⁻¹( x )

Options

  1. Ais given by x-3 2
  2. Bis given by 1 2 x+3
  3. Cdoes not exist because ' P ' is not injective
  4. Ddoes not exist because ' P is not surjective

Correct answer

A. is given by x-3 2

Step-by-step solution

Let x ₁, x ₂ R array lrl Let & f ( x ₁ ) & = f ( x ₂ ) & 2 x ₁+3 & =2 x ₂+3 & x ₁ & = x ₂ array Hence, f is injective. Let y codomain R array ll Let & y=f(x) & y=2 x+3 & x= y-3 2 domain R array Hence, f is onto (surjective). f ⁻¹ exists. f ⁻¹( x )= x -3 2 , x R

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