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AP EAMCET2002MathematicsFunctions

If the functions f and g are defined by f(x)=3 x-4, g(x)=2+3 x for x R respective, then g⁻¹ (f⁻¹(5) ) is equal to

Options

  1. A1
  2. B1 2
  3. C1 3
  4. D1 4

Correct answer

C. 1 3

Step-by-step solution

We have, aligned & f(x)=3 x-4=y & 3 x=y+4 x= y+4 3 & f⁻¹(y)= y+4 3 & and g(x)=2+3 x=z & 3 x=z-2 & x= z-2 3 & g⁻¹(z)= z-2 3 & g⁻¹ (f⁻¹(5) )=g⁻¹ [ 5+4 3 ]=g⁻¹[3] & = 3-2 3 = 1 3 & aligned

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