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Algebra Level pending

Let f ( x ) = x + 1 f(x) = x + 1 and g ( x ) = k x 3 g(x) = kx^3 . Find the value of k k given that f g ( 3 ) = 55 fg(3) = 55 .


The answer is 2.

Noel Lo by Noel Lo , 24, Singapore

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1 solution

Noel Lo
Apr 6, 2015

f g ( 3 ) = f ( k × 3 3 ) = f ( 27 k ) = 27 k + 1 fg(3) = f(k\times 3^3) = f(27k) = 27k + 1

27 k + 1 = 55 27k +1 =55

27 k = 54 27k = 54

k = 54 27 = 2 k = \frac{54}{27} = \boxed{2}

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