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AP EAMCET2015MathematicsFunctions

If f: R R, g: R R are defined by f(x)=5 x-3, g(x)=x^2+3 , then g f⁻¹(3) is equal to

Options

  1. A25 3
  2. B111 25
  3. C9 25
  4. D25 111

Correct answer

B. 111 25

Step-by-step solution

Given, f(x)=5 x-3 and g(x)=x^2+3 Let, y=f(x), y=5 x-3 aligned & y+3=5 x x= y+3 5 & f⁻¹(y)= y+3 5 f⁻¹(x)= x+3 5 aligned Now, g(x)=x^2+3 ; So, g f⁻¹(3)=g [f⁻¹(3) ] =g ( 3+3 5 )=g ( 6 5 )= (6)^2 (5)^2 +3= 36 25 +3= 111 25

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