functions

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If f ( x ) = x 2 + 3 f(x)= x^2 + 3 , find the function g g such that g ∘ f ( x ) = 2 x 2 + 3 g\circ f(x)= 2x^2 + 3 .

g(x) = 2x - 3 g(x) = 3x - 6 g(x) = 4 - x g(x) = x+ 2

Mashruk Anim by Mashruk Anim , 30, Bangladesh

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1 solution

Finn Hulse
Apr 13, 2014

Let's set it up: g ( 2 x 2 + 3 ) g(2x^2+3) . For the coefficient of x 2 x^2 to go from one to two, we have to have multiplied by two in g ( x ) g(x) . Plugging f ( x ) f(x) into g ( x ) = 2 x g(x)=2x produces 2 x 2 + 6 2x^2+6 , which is three more than the desired. Thus, g ( x ) g(x) must be 2 x − 3 \boxed{2x-3} .

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