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KCET2023MathematicsFunctions

Let f : R R be defined by f(x)=3 x^2-5 and g: R R by g(x)= x x^2+1 , then g f is

Options

  1. A3 x^2-5 9 x^4-6 x^2+26
  2. B3 x^2 x^4+2 x^2-4
  3. C3 x^2 9 x^4+30 x^2-2
  4. D3 x^2-5 9 x^4-30 x^2+26

Correct answer

D. 3 x^2-5 9 x^4-30 x^2+26

Step-by-step solution

Given that f(x)=3 x^2-5 and g(x)= x x^2+1 g o t=g f(x) =g (3 x^2-5 ) aligned & = 3 x^2-5 (3 x^2-5 )^2+1 = 3 x^2-5 9 x^4-30 x^2+25+1 & = 3 x^2-5 9 x^4-30 x^2+26 aligned

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