Q(a+1) - 2q(a) if q(x) = x²+3x+4

The expression for q(a+1) - 2q(a) is -a² - a

Given the expression q(x) = x²+3x+4

First, we need to get the function q(a+1)

q(a+1) =  (a+1)²+3(a+1)+4

Expand

q(a+1) = a² + 2a + 1 + 3a + 3 + 4

q(a+1) = a² + 5a + 8

For the function q(a)

q(a) = a²+3a+4

2q(a) = 2(a²+3a+4)

2q(a)= 2a² + 6a + 8

Taking the difference:

q(a+1) - 2q(a) = a² + 5a + 8 - ( 2a² + 6a + 8)

q(a+1) - 2q(a)  = a² + 5a + 8 -  2a² - 6a - 8

q(a+1) - 2q(a)  = -a² - a

Hence the expression for q(a+1) - 2q(a) is -a² - a

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Step(1)

To find q(a) we just need to put a instead of x in q(x) function.

Let's do it...

Multiply sides by -2 :

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Step (2)

To find q(a+1) we just need to put a+1 instead of x in q(x) function.

Let's do it...

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Step (3)

And we're done.

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