Determine f(x) if 2*f(x) + 3*f(1-x) = 4x - 1

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2*f(x) +  3*f(1-x) = 4x-1

We notice that f(x) is a linear function:

==> let f(x) = ax+b

==> f(1-x) = a(1-x) + b = a - ax + b = -ax + a+b

Now substiute :

==> 2(ax+b) + 3(-ax+a+b) = 4x - 1

==> 2ax + 2b - 3ax...

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2*f(x) +  3*f(1-x) = 4x-1

We notice that f(x) is a linear function:

==> let f(x) = ax+b

==> f(1-x) = a(1-x) + b = a - ax + b = -ax + a+b

Now substiute :

==> 2(ax+b) + 3(-ax+a+b) = 4x - 1

==> 2ax + 2b - 3ax + 3a + 3b = 4x-1

==>  ax + 3a +5b  = 4x - 1

==> a= 4

==> 3a + 5b = -1

==> 12 + 5b = -1

==> 5b = 11

==> b= 11/5

==> f(x) = 4x + 11/5

 

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