Functions

Algebra Level 3

Define f ( x ) = 2 x + 3 f(x)=2x+3 and suppose that g ( x + 2 ) = f ( f ( x − 1 ) ⋅ f ( x + 1 ) + f ( x ) ) g(x+2)=f(f(x-1)\cdot f(x+1)+f(x)) then what is g ( 6 ) = ? g (6)=?


The answer is 259.

Hana Wehbi by Hana Wehbi , 51, USA

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1 solution

David Vreken
Dec 18, 2018

g ( 6 ) g(6)

= g ( 4 + 2 ) = g(4 + 2)

= f ( f ( 4 − 1 ) ⋅ f ( 4 + 1 ) + f ( 4 ) ) = f(f(4 - 1) \cdot f(4 + 1) + f(4))

= f ( f ( 3 ) ⋅ f ( 5 ) + f ( 4 ) ) = f(f(3) \cdot f(5) + f(4))

= f ( ( 2 ⋅ 3 + 3 ) ⋅ ( 2 ⋅ 5 + 3 ) + ( 2 ⋅ 4 + 3 ) ) = f((2 \cdot 3 + 3) \cdot (2 \cdot 5 + 3) + (2 \cdot 4 + 3))

= f ( 9 ⋅ 13 + 11 ) = f(9 \cdot 13 + 11)

= f ( 128 ) = f(128)

= 2 ⋅ 128 + 3 = 2 \cdot 128 + 3

= 259 = \boxed{259}

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Thank you for sharing your solution.

Hana Wehbi - 2 years, 5 months ago

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