Function problem 2

Algebra Level 2

We have a function f ( x ) = 4 x + c f(x)=4x+c and f ( g ( x ) ) = 12 x + d f(g(x))=12x+d . If g ( x ) = c x + 2 g(x)=cx+2 , find d d .


The answer is 11.

Anatoly Safiulov by Anatoly Safiulov , 18, United Kingdom

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1 solution

Samrit Pramanik
Jun 9, 2018

f ( g ( x ) ) = 4 c x + 8 + c = 12 x + d f\left( g(x)\right) = 4cx+8+c=12x+d

As this an identity, equating the coefficient of x x both side, we finally get

4 c = 12 ⇒ c = 3 4c=12 \Rightarrow c=3 and 8 + c = d ⇒ d = 11 8+c=d \Rightarrow d=\boxed{11}

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