Find the function calculate f(6)

label Algebra
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i. F(1)=1

ii. F(2x)= 4f(x)+6

iii. F(x+2) = f(x)+12x+12

Calculate f(6)

Sep 2nd, 2015

Thank you for the opportunity to help you with your question!

F(1)=1

F(2x)=4f(x)+6

f(x+2)=f(x)+12x+1

Note, we can use the facts from these three equations. Note, we know that F(1)=1.

Therefore, let's substitute in f(1)=1 into  f(x+2)=f(x)+12x+1

Therefore when we substitute (as follows) we see

f(1+2)=f(1)+12(1)+1

f(3)=1+12(1)+1

f(3)=14

we now found f(3)=14.

Now we substitute f(3)=14 into the other equation f(2x)=4f(x)+6

f(2*3)= 4f(3)+6

f(6)=4(14)+6

f(6)=62


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Sep 2nd, 2015

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