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Amanda [17]
2 years ago
14

Determine g(x + a) – g(x) for the following function. g(x) = 5x2 + 2x

Mathematics
1 answer:
dusya [7]2 years ago
3 0

Answer:

g(x + a) - g(x) = 10ax + 5a^2 + 2a

Step-by-step explanation:

We are given the function:

g(x) = 5x^2 + 2x

And we want to determine:

\displaystyle g(x+a) - g(x)

Substitute:

\displaystyle \begin{aligned}g(x + a) - g(x) &=\left[5(x+a)^2 + 2(x+a)\right] -\left[5x^2+2x\right]    \end{aligned}

And simplify:

\displaystyle \begin{aligned}g(x + a) - g(x) &=\left[5(x+a)^2 + 2(x+a)\right] -\left[5x^2+2x\right] \\  \\ &= \left(5(x^2 + 2ax + a^2) + (2x + 2a) \right) + \left(-5x^2 - 2x\right) \\ \\ &= \left((5x^2 + 10ax + 5a^2) + (2x + 2a)\right) + \left(-5x^2 - 2x\right) \\ \\ &= (5x^2-5x^2) + (10ax + 2x - 2x) + (5a^2+2a)     \\ \\ &= 10ax + 5a^2 + 2a \end{aligned}

In conclusion:

g(x + a) - g(x) = 10ax + 5a^2 + 2a

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