If f(x)=4x-x^2, x , then write the value of f(a + 1) - f(a - 1). - Vidyadip

Question

If $\text{f(x)}=4\text{x}-\text{x}^2,\text{ x}\in\text{R},$ then write the value of f(a + 1) - f(a - 1).

✓

Answer

We have,
f(x) = 4x - x²
Now, f(a + 1) = 4(a + 1) - (a + 1)²
= 4a + 4 - a² - 1 - 2a
= -a²+ 3 + 2a
⇒ f(a + 1) = -a² + 2a + 3 ...(i)
and, f(a - 1) = 4(a - 1) - (a - 1)²
= 4a - 4 - (a² + 1 - 2a)
= 4a - 4 - a² - 1 + 2a
= 6a - a - 5
f(a - 1) = -a² + 6a - 5 ....(ii)
Subtracting equation (ii) from equation (i), we get
f(a + 1) - f(a - 1)
= -a² + 2a + 3 - (-a² + 6a - 5)
= -a² + 2a + 3 + a² - 6a + 5
= -4a + 8 = 4(2 - a)

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