2 variable function

Calculus Level 4

A function in x and y is defined as, f(x) +f(2x+y) +5xy = f(3x-y) +2x^2 + 1.Find the value of f(2015) in terms of $a{ x }^{ b }+c$ . Then find x-2a-b+c.

cannot be written as

a{ x }^{ b }+c

2016 2015 2014

1 solution

Nelson Mandela
Jul 18, 2015

just take y as x/2. then, we get f(x) = $2{ x }^{ 2 }-\frac { 5 }{ 2 } { x }^{ 2 }+1$ .

So, f(x) = $1-\frac { { x }^{ 2 } }{ 2 }$ .

So, f(2015) = $1-\frac { { 2015 }^{ 2 } }{ 2 }$ .

Hence, a=-0.5, b=2, c=1 and x = 2015.

so 2015+1-2+1=2015.

2 variable function

1 solution

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