Function this to work

Algebra Level 2

If f ( 3 x + 1 ) = 6 x + 3 f(3x + 1) = 6x + 3 , find f ( − 1 ) + f ( − 5 ) f(-1)+f(-5)


The answer is -10.

Jason Chrysoprase by Jason Chrysoprase , 18, Indonesia

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1 solution

Hung Woei Neoh
Jun 12, 2016

We need to find the values of x x that gives us f ( 3 x + 1 ) = f ( − 1 ) f(3x+1)=f(-1) and f ( 3 x + 1 ) = f ( − 5 ) f(3x+1)=f(-5)

3 x + 1 = − 1 3 x = − 2 x = − 2 3 ⟹ f ( − 1 ) = 6 ( − 2 3 ) + 3 = − 1 3x+1=-1\\ 3x=-2\\ x=-\dfrac{2}{3}\\ \implies f(-1) = 6\left(-\dfrac{2}{3}\right) + 3 = -1

3 x + 1 = − 5 3 x = − 6 x = − 2 ⟹ f ( − 5 ) = 6 ( − 2 ) + 3 = − 9 3x+1 = -5\\ 3x=-6\\ x=-2\\ \implies f(-5) = 6(-2)+3 = -9

Therefore, f ( − 1 ) + f ( − 5 ) = − 1 + ( − 9 ) = − 10 f(-1) + f(-5) = -1 + (-9) = \boxed{-10}

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